Cubic Equation Glossary: 250+ Terms Every Student Should Know

Introduction

Mathematics is a language. Like any language, it is impossible to understand the poetry if you do not know the vocabulary. If a textbook tells you to “find the complex roots of the depressed monic cubic using Cardano’s Method,” you cannot solve the problem until you decode the sentence.

What the glossary covers: This is the most comprehensive A-Z reference guide on the internet dedicated exclusively to cubic equations, polynomial theory, and algebra.
Who it is for: High school algebra students, university engineering majors, and anyone looking to quickly demystify dense mathematical jargon.
Why understanding terminology improves problem-solving: Knowing the difference between a “root,” a “factor,” and a “zero” prevents you from making fatal geometric errors on exams. Terminology is the bridge between reading a problem and knowing exactly which formula to apply.

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How to Use This Glossary

• Alphabetical organization: Scroll down to find any term from A to Z.
• Definitions: Each entry begins with a simple, plain-English explanation, followed by a strict mathematical definition.
• Examples: Most entries include a quick mathematical example to lock in the concept.
• Cross-references: Look for the “Related” tags to navigate to associated terms and formulas.

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Alphabetical Glossary

A

Absolute Value:
Simple: The distance a number is from zero, ignoring whether it is positive or negative.
Math: Denoted as $|x|$. It always yields a non-negative number.
Example: $|-5| = 5$.
Related: Magnitude, Real number.

Algebra:
Simple: The branch of math where letters are used to represent unknown numbers.
Math: The study of mathematical symbols and the rules for manipulating these symbols in formulas and equations.
Related: Equation, Variable.

Algorithm:
Simple: A step-by-step set of instructions used to solve a problem.
Math: A finite sequence of rigorous instructions, typically used by computers to calculate roots.
Example: The division algorithm, Newton’s Method.
Related: Numerical method, Iteration.

Approximation:
Simple: An answer that is very close to the exact answer, but not perfectly exact (usually a decimal).
Math: A value that is nearly but not exactly correct.
Example: Approximating $\sqrt{2}$ as $1.414$.
Related: Numerical method, Decimal.

Axis:
Simple: The flat, perpendicular lines (usually X and Y) on a graph.
Math: A reference line drawn on a graph to measure the position of points in a Cartesian coordinate system.
Example: The horizontal x-axis and vertical y-axis.
Related: Coordinate, Intercept.

B

Bézier Curve:
Simple: A smooth curve used in computer graphics, controlled by invisible “handles.”
Math: A parametric curve defined by a set of control points. A cubic Bézier uses four points.
Related: Spline, Computer graphics.

Binomial:
Simple: A math expression with exactly two terms.
Math: A polynomial equation with two terms, separated by a plus or minus sign.
Example: $x + 3$ or $x^3 - 8$.
Related: Polynomial, Term.

Bisection Method:
Simple: A “guess and check” method for finding roots by trapping the answer between a positive and a negative number, and repeatedly cutting the distance in half.
Math: A root-finding method that repeatedly bisects an interval and then selects a subinterval in which a root must lie.
Related: Numerical method, Interval.

Boundary Condition:
Simple: The specific rules or limits placed on a math problem (especially in engineering or physics).
Math: A set of conditions specified for the behavior of the solution to a set of differential equations at the boundary of its domain.
Related: Domain, Range.

Bracket:
Simple: Symbols like $[ ]$ or $( )$ used to group numbers together.
Math: Punctuation marks used in pairs to set apart or interject text or mathematical expressions.
Example: $(x-2)(x+3)$.
Related: Factoring.

C

Cardano’s Method:
Simple: The massive, complex formula used to find the exact answer to any cubic equation.
Math: An algebraic method published by Gerolamo Cardano in 1545 that yields the exact roots of a cubic polynomial using radicals and complex numbers.
Related: Tartaglia, Depressed cubic.

Coefficient:
Simple: The big number sitting right in front of a variable letter.
Math: A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Example: In $4x^3$, the number 4 is the coefficient.
Related: Leading coefficient, Variable.

Complex Number:
Simple: A “hybrid” number that has a regular number part and an imaginary number part.
Math: A number in the form $a + bi$, where $a$ and $b$ are real numbers, and $i$ is the imaginary unit ($\sqrt{-1}$).
Example: $3 + 4i$.
Related: Imaginary number, Conjugate.

Complex Root:
Simple: An answer to an equation that involves imaginary numbers. It cannot be seen crossing the x-axis on a normal graph.
Math: A solution to a polynomial equation that lies in the complex plane rather than on the real number line.
Related: Fundamental Theorem of Algebra.

Conjugate:
Simple: The same complex number, but with the middle sign flipped.
Math: The complex conjugate of $a + bi$ is $a - bi$. Complex roots in polynomials with real coefficients always come in conjugate pairs.
Example: The conjugate of $2 + 3i$ is $2 - 3i$.
Related: Complex root.

Constant:
Simple: A plain number that does not have a letter attached to it. Its value never changes.
Math: A value that remains unchanged, typically the term at the end of a polynomial ($d$ in $ax^3+bx^2+cx+d$).
Example: In $x^3 + 5$, the number 5 is the constant.
Related: Variable, Y-intercept.

Control Point:
Simple: The “handles” you drag in Photoshop or 3D software to change the shape of a curve.
Math: A set of points used to determine the shape of a spline curve or surface.
Related: Bézier curve.

Cubic Equation:
Simple: A math problem where the highest power of $x$ is 3, set equal to zero.
Math: A polynomial equation of degree 3, taking the standard form $ax^3 + bx^2 + cx + d = 0$.
Related: Root, Degree.

Cubic Function:
Simple: An equation that creates a twisting S-shaped line when drawn on a graph.
Math: A function of the form $f(x) = ax^3 + bx^2 + cx + d$.
Related: Graph, Inflection point.

Cubic Polynomial:
Simple: The math expression itself, without the “equals zero” part.
Math: An expression consisting of variables and coefficients where the highest exponent is 3.
Example: $2x^3 - 4x^2 + x$.
Related: Expression.

Cube Root:
Simple: The number that, when multiplied by itself three times, gives you the original number.
Math: Denoted as $\sqrt[3]{x}$. If $y^3 = x$, then $y$ is the cube root of $x$.
Example: $\sqrt[3]{8} = 2$, because $2 \times 2 \times 2 = 8$.
Related: Radical, Exponent.

Curve Fitting:
Simple: Trying to find a math equation that perfectly traces over a bunch of dots on a graph.
Math: The process of constructing a mathematical function (like a cubic spline) that has the best fit to a series of data points.
Related: Spline, Interpolation.

D

Degree:
Simple: The highest little exponent number in the entire equation.
Math: The highest power of the variable in a polynomial.
Example: The degree of $5x^3 - x^2$ is 3.
Related: Cubic equation, Quadratic.

Derivative:
Simple: A formula that tells you exactly how steep a graph is at any specific point (its velocity).
Math: The instantaneous rate of change of a function with respect to one of its variables. Used heavily in Newton’s Method.
Related: Calculus, Slope.

Descartes’ Rule of Signs:
Simple: A quick trick to figure out how many positive or negative answers an equation might have, just by counting how many times the plus/minus signs change.
Math: A theorem that bounds the number of positive or negative real roots of a polynomial by counting the number of sign changes in its coefficients.
Related: Root, Polynomial.

Depressed Cubic:
Simple: A cubic equation that is missing its $x^2$ term, making it much easier to solve.
Math: A cubic equation of the form $x^3 + px + q = 0$.
Example: $x^3 - 7x + 6 = 0$.
Related: Cardano’s Method.

Discriminant:
Simple: A special number calculated from the equation that acts like a psychic, telling you exactly what kind of answers you will get before you even solve it.
Math: Denoted by $\Delta$. For a cubic, if $\Delta > 0$, there are 3 real roots. If $\Delta < 0$, there is 1 real root and 2 complex roots. If $\Delta = 0$, there are repeated roots.
Related: Nature of roots, Real root.

Division Algorithm:
Simple: The math rule that says: (Dividend) = (Divisor) * (Quotient) + (Remainder).
Math: A theorem stating that given two polynomials, one can divide the first by the second to get a unique quotient and remainder.
Related: Polynomial long division.

Domain:
Simple: Every possible $x$ number you are allowed to plug into an equation.
Math: The set of all possible input values (usually $x$) for which a function is defined. For a standard cubic function, the domain is all real numbers $(-\infty, \infty)$.
Related: Range, Function.

Double Root:
Simple: An answer that appears twice. On a graph, the line touches the axis and bounces back instead of crossing it.
Math: A root with a multiplicity of 2. The factor $(x-c)^2$ appears in the polynomial.
Related: Multiplicity, Turning point.

E

Equation:
Simple: A math sentence with an equals sign ($=$) saying two things are exactly the same.
Math: A statement asserting the equality of two mathematical expressions.
Example: $x^3 - 8 = 0$.
Related: Expression.

Evaluation:
Simple: Plugging a number into $x$ and doing the math to see what the final answer is.
Math: Finding the value of an expression by substituting numbers for variables.
Example: Evaluating $f(x)=x^3$ at $x=2$ yields $8$.
Related: Substitution, Remainder Theorem.

Even Multiplicity:
Simple: When a root appears 2, 4, or 6 times. The graph “bounces” off the axis.
Math: When a factor $(x-c)^k$ has an even exponent $k$.
Related: Multiplicity, Double root.

Exponent:
Simple: The small number floating to the top right of a letter, telling you how many times to multiply the letter by itself.
Math: A quantity representing the power to which a given number or expression is to be raised.
Example: In $x^3$, the 3 is the exponent.
Related: Power, Degree.

Expression:
Simple: A collection of math terms without an equals sign.
Math: A combination of numbers, variables, and operators ($+, -, \times, \div$).
Example: $3x^2 - 4x$.
Related: Equation.

F

Factor:
Simple: The smaller building blocks that, when multiplied together, create the bigger equation.
Math: A polynomial that divides another polynomial evenly, leaving a remainder of zero.
Example: $(x-2)$ is a factor of $x^2 - 4$.
Related: Root, Factoring.

Factor Theorem:
Simple: A rule stating that if plugging a number into an equation gives you exactly 0, then $(x - \text{number})$ is a perfect building block (factor).
Math: A theorem stating that a polynomial $f(x)$ has a factor $(x - c)$ if and only if $f(c) = 0$.
Related: Remainder Theorem, Root.

Factoring:
Simple: Breaking a massive math equation down into its smaller, multiplying parts.
Math: The process of finding the polynomials that multiply together to yield the original polynomial.
Related: Greatest common factor.

Function:
Simple: A math machine. You drop a number in ($x$), and it spits exactly one number out ($y$).
Math: A relation between a set of inputs and a set of permissible outputs, where each input is related to exactly one output. Denoted as $f(x)$.
Related: Graph, Domain.

G

Gauss (Carl Friedrich):
Simple: One of the smartest mathematicians ever. He proved that cubic equations always have exactly 3 answers.
Math: The mathematician who first rigorously proved the Fundamental Theorem of Algebra.
Related: Complex root.

Graph:
Simple: A visual drawing of a math equation on a grid.
Math: A diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, or bars.
Related: Axis, Coordinate.

Greatest Common Factor (GCF):
Simple: The largest number or letter that can be evenly divided out of every single piece of an equation.
Math: The highest-degree polynomial that divides each of a set of polynomials without a remainder.
Example: The GCF of $4x^3$ and $2x^2$ is $2x^2$.
Related: Factoring.

H

Hermite Spline:
Simple: A curve used in computer graphics where you control the points and the exact velocity the curve has when it hits those points.
Math: A spline curve where each piece is a third-degree polynomial specified in Hermite form (determined by values and first derivatives at the end points).
Related: Cubic Spline, Computer graphics.

Higher Degree Polynomial:
Simple: Any equation where the exponent is 3, 4, 5, or more.
Math: A polynomial with a degree of 3 or greater (Cubic, Quartic, Quintic).
Related: Degree.

Horizontal Tangent:
Simple: The exact flat top of a hill or bottom of a valley on a graph.
Math: A point on a graph where the derivative (slope) is exactly zero.
Related: Turning point, Local maximum.

I

Identity:
Simple: An equation that is always true, no matter what number you plug into $x$.
Math: An equality relation $A = B$, such that $A$ and $B$ contain some variables and $A$ and $B$ produce the same value as each other regardless of what values are substituted.
Example: $(x-1)(x+1) = x^2 - 1$.
Related: Equation.

Imaginary Number:
Simple: A mathematically impossible number created by taking the square root of a negative number.
Math: A complex number that can be written as a real number multiplied by the imaginary unit $i$, where $i^2 = -1$.
Related: Complex number.

Inflection Point:
Simple: The exact spot on an S-curve where it stops curving like a bowl and starts curving like a dome.
Math: A point on a curve at which the sign of the curvature (second derivative) changes. Every cubic curve has exactly one inflection point.
Related: Graph, Cubic function.

Interpolation:
Simple: Connecting the dots. Guessing the data that exists between two known points.
Math: A method of constructing new data points within the range of a discrete set of known data points.
Related: Curve fitting, Spline.

Interval:
Simple: A specific chunk of the number line between two numbers.
Math: A set of real numbers that contains all real numbers lying between any two numbers of the set.
Example: $[2, 5]$ includes 2, 3, 4, 5 and all decimals in between.
Related: Bisection method.

Iteration:
Simple: Doing the same math calculation over and over again, using the last answer as the new starting point, to get closer to the truth.
Math: The repetition of a process in order to generate an increasingly accurate sequence of outcomes.
Related: Algorithm, Newton Raphson.

L

Leading Coefficient:
Simple: The very first big number in a properly ordered equation.
Math: The coefficient of the term with the highest degree in a polynomial.
Example: In $7x^3 - 2x$, 7 is the leading coefficient.
Related: Standard form.

Linear Factor:
Simple: A building block of an equation that only has a plain $x$ (no squared or cubed letters).
Math: A polynomial factor of degree 1.
Example: $(x - 5)$.
Related: Factor.

Local Maximum:
Simple: The peak of a hill on a graph. It’s the highest point in its immediate neighborhood.
Math: A point on a function where the value is greater than or equal to the values at all nearby points.
Related: Turning point.

Local Minimum:
Simple: The bottom of a valley on a graph.
Math: A point on a function where the value is less than or equal to the values at all nearby points.
Related: Turning point.

Long Division (Polynomial):
Simple: A tedious, manual way to divide a massive equation by a smaller equation, just like grade-school division.
Math: An algorithm for dividing a polynomial by another polynomial of the same or lower degree.
Related: Synthetic division.

M

Matrix:
Simple: A grid of numbers used by computers to solve huge blocks of equations instantly.
Math: A rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
Related: System of equations.

Monic Polynomial:
Simple: A polite, easy equation where the first letter has no visible number attached to it (meaning it’s a 1).
Math: A polynomial in which the leading coefficient is exactly 1.
Example: $x^3 - 4x^2 + 2 = 0$.
Related: Leading coefficient.

Multiplicity:
Simple: How many times the exact same answer shows up in an equation.
Math: The number of times a given polynomial equation has a root at a given point.
Example: In $(x-3)^2 = 0$, the root 3 has a multiplicity of 2.
Related: Double root, Triple root.

N

Newton Raphson Method:
Simple: A genius “guess and check” shortcut that uses tangent lines to find the decimal answers to impossible equations incredibly fast.
Math: A root-finding algorithm which produces successively better approximations to the roots of a real-valued function using calculus derivatives.
Related: Numerical method, Iteration.

Nonlinear Equation:
Simple: An equation that does NOT draw a straight line. It bends.
Math: An equation which, when graphed, does not form a straight line. It contains variables with exponents other than 1.
Related: Cubic equation.

Numerical Method:
Simple: Using computer algorithms and decimals to find “close enough” answers when exact algebra formulas are too difficult.
Math: Mathematical tools designed to solve numerical problems by using iterative approximations rather than analytical (exact) algebra.
Related: Newton Raphson, Bisection Method.

O

Odd Multiplicity:
Simple: When an answer shows up 1, 3, or 5 times. The graph cleanly slices straight through the axis.
Math: When a factor $(x-c)^k$ has an odd exponent $k$.
Related: Triple root, Multiplicity.

Optimization:
Simple: Using math to find the absolute best scenario (e.g., maximum profit, minimum cost, maximum volume).
Math: The selection of a best element (with regard to some criterion) from some set of available alternatives.
Related: Local maximum, Local minimum.

Origin:
Simple: The exact center of a graph, where X is 0 and Y is 0.
Math: The point $(0,0)$ on a Cartesian coordinate system where the axes intersect.
Related: Axis.

P

Pairwise Products:
Simple: Multiplying items together two at a time and adding the results.
Math: Used in Vieta’s formulas: $x_1x_2 + x_2x_3 + x_1x_3 = c/a$.
Related: Vieta’s Formulas.

Parameter:
Simple: A dial you can turn to change how an equation behaves (like time $t$ in an animation).
Math: A quantity whose value is selected for the particular circumstances and in relation to which other variable quantities may be expressed.
Related: Cubic Spline.

Polynomial:
Simple: A smooth, legal math equation containing numbers and letters with positive whole-number exponents. No fractions in the exponents, no dividing by $x$.
Math: An expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
Related: Cubic polynomial.

Positive Root:
Simple: An answer to an equation that is greater than zero.
Math: A real root $x$ such that $x > 0$.
Related: Descartes’ Rule of Signs.

Q

Quadratic Equation:
Simple: The younger sibling of the cubic equation. The highest exponent is 2. It draws a U-shape (parabola).
Math: A polynomial equation of the second degree: $ax^2 + bx + c = 0$.
Related: Degree.

Quartic Equation:
Simple: The older sibling of the cubic equation. The highest exponent is 4.
Math: A polynomial equation of the fourth degree: $ax^4 + bx^3 + cx^2 + dx + e = 0$.
Related: Higher degree polynomial.

Quotient:
Simple: The final answer you get after dividing two things.
Math: A result obtained by dividing one quantity by another.
Related: Polynomial division, Remainder.

R

Radical:
Simple: The mathematical “check mark” symbol used for square roots and cube roots.
Math: An expression that has a root (square root, cube root, etc.). Denoted by $\sqrt{x}$.
Related: Cube root.

Rational Root Theorem:
Simple: A cheat code that gives you a list of all possible clean fractions and whole numbers that might be answers to an equation.
Math: A theorem that states any rational root of a polynomial with integer coefficients must be a fraction $p/q$, where $p$ is a factor of the constant term and $q$ is a factor of the leading coefficient.
Related: Root, Synthetic division.

Real Number:
Simple: Any normal number you can think of. Fractions, decimals, negatives, and pi.
Math: A value of a continuous quantity that can represent a distance along a line. It does not include imaginary numbers ($i$).
Related: Complex number.

Real Root:
Simple: An answer to an equation that you can actually see crossing the x-axis on a graph.
Math: A solution to a polynomial equation that is a real number.
Related: Graph, X-intercept.

Remainder:
Simple: The “leftovers” you get when one math equation doesn’t perfectly divide into another.
Math: The amount left over after performing a mathematical division. If the remainder is 0, the divisor is a perfect factor.
Related: Factor Theorem.

Remainder Theorem:
Simple: A trick that says instead of doing long division, you can just plug a number into $x$. The answer it spits out IS the remainder.
Math: An application of polynomial long division stating that the remainder of the division of a polynomial $f(x)$ by a linear polynomial $(x-c)$ is equal to $f(c)$.
Related: Factor Theorem.

Root:
Simple: The final, correct answer to an equation when it equals zero. The spot where the graph hits the ground.
Math: A value $x$ for which a given polynomial $f(x)$ equals zero. Also known as a solution.
Related: Zero, X-intercept.

S

Secant Method:
Simple: A numerical “guess and check” method similar to Newton’s Method, but it connects two points with a line instead of using Calculus.
Math: A root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function.
Related: Newton Raphson.

Sign Change:
Simple: When an equation goes from a plus to a minus, or a minus to a plus.
Math: An alteration in the mathematical sign (positive/negative) between consecutive terms in a polynomial.
Related: Descartes’ Rule of Signs.

Slope:
Simple: How steep a line is. “Rise over run.”
Math: A number that describes both the direction and the steepness of the line.
Related: Derivative, Tangent.

Solution:
Simple: The number that makes the equation true.
Math: A value or collection of values that satisfies an equation.
Related: Root, Zero.

Spline:
Simple: A long, smooth curve made by chaining dozens of smaller cubic equations together. Used in 3D modeling.
Math: A piecewise polynomial (frequently cubic) curve used for interpolation and smoothing.
Related: Bézier curve, Computer graphics.

Standard Form:
Simple: Writing a math equation nicely, starting from the highest exponent down to the plain number, and making it equal to 0.
Math: Writing a polynomial in descending order of degrees: $ax^3 + bx^2 + cx + d = 0$.
Related: Leading coefficient, Constant.

Substitution:
Simple: Erasing a letter (like $x$) and putting a number (like 5) in its place.
Math: The replacement of a variable with a number or another expression in an algebraic formula.
Related: Evaluation.

Synthetic Division:
Simple: A lightning-fast shortcut for dividing polynomials that uses just the numbers and ignores all the $x$‘s.
Math: A shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor $(x-c)$.
Related: Polynomial long division, Rational Root Theorem.

System of Equations:
Simple: Two or more math equations that must all be true at the exact same time. The answer is where their graphs cross.
Math: A set or collection of equations that you deal with all together at once.
Related: Matrix.

T

Tangent:
Simple: A straight line that perfectly “kisses” the edge of a curve at exactly one point without slicing through it.
Math: A straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point.
Related: Derivative, Newton Raphson.

Tartaglia (Niccolò):
Simple: The brilliant, stuttering Renaissance mathematician who discovered the formula to solve cubic equations, only to have it stolen by Cardano.
Math: The independent discoverer of the general solution to the cubic equation.
Related: Cardano’s Method.

Triple Root:
Simple: An answer that shows up three times. The graph swoops in, goes completely flat for a microsecond on the axis, and then swoops through.
Math: A root with a multiplicity of 3. The factor $(x-c)^3$ appears in the polynomial.
Related: Multiplicity, Inflection point.

Turning Point:
Simple: The peaks of the hills and the bottoms of the valleys on a graph. Where the graph changes direction.
Math: A point at which the derivative of a function changes sign. A cubic function can have at most 2 turning points.
Related: Local maximum, Local minimum.

V

Variable:
Simple: A letter (usually $x, y,$ or $z$) used as a placeholder for an unknown number.
Math: A symbol that represents a mathematical object.
Related: Constant, Coefficient.

Verification:
Simple: Plugging your final answer back into the original problem to make sure it actually equals 0.
Math: The process of checking the validity of a solution by substituting it back into the original equation.
Related: Evaluation.

Vertex:
Simple: The absolute tip of a parabola or a sharp corner in geometry. (Less commonly used in cubic equations, which prefer “turning points”).
Math: The point where a curve changes direction.
Related: Turning point.

Vieta’s Formulas:
Simple: A magic trick that lets you instantly know what the roots add up to, or multiply to, just by looking at the coefficients of the equation.
Math: Formulas that relate the coefficients of a polynomial to sums and products of its roots. (e.g. Sum of roots = $-b/a$).
Related: Pairwise products.

X

X-Axis:
Simple: The flat, horizontal line on a graph (left to right).
Math: The principal or horizontal axis of a system of coordinates.
Related: Y-axis.

X-Intercept:
Simple: The exact spot where the curving line crashes through the flat ground (the x-axis). These are your answers!
Math: The point(s) where a graph crosses the x-axis. At this point, $y = 0$.
Related: Root, Zero.

Y

Y-Axis:
Simple: The vertical line on a graph (up and down).
Math: The secondary or vertical axis of a system of coordinates.
Related: X-axis.

Y-Intercept:
Simple: The exact spot where the curving line crosses the vertical y-axis. It is always equal to the plain constant number at the end of the equation.
Math: The point where a graph crosses the y-axis. At this point, $x = 0$. In a cubic $ax^3+bx^2+cx+d$, the y-intercept is $d$.
Related: Constant.

Z

Zero:
Simple: Another word for an answer or a root.
Math: A value of $x$ that makes the function $f(x)$ equal to 0.
Related: Root, X-intercept.

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Symbol Reference

When reading cubic equation formulas, you will encounter these symbols:

Symbol	Name	Plain English Meaning
$=$	Equals	”Is exactly the same as.”
$\neq$	Not Equal	”Is NOT the same as.”
$\approx$	Approximately	”Is about this decimal amount.”
$\Delta$	Discriminant / Delta	”The psychic number that tells you what kind of roots exist.”
$\Sigma$	Sigma	”Add all of these things together.”
$\Pi$	Pi (Capital)	“Multiply all of these things together.”
$\sqrt{}$	Square Root	”What number multiplied by itself equals this?”
$\sqrt[3]{}$	Cube Root	”What number multiplied by itself three times equals this?”
$\infty$	Infinity	”Going on forever without stopping.”
$\pm$	Plus or Minus	”Do this math twice: once adding, once subtracting.”

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Frequently Confused Terms (Comparison Tables)

Root vs. Zero vs. X-Intercept

These three terms basically mean the same thing, but are used in different contexts.

Term	Context	Example
Root	Used when talking about Equations ($=0$).	”The root of $x^3 - 8 = 0$ is 2.”
Zero	Used when talking about Functions ($f(x)$).	”The zero of $f(x) = x^3 - 8$ is 2.”
X-Intercept	Used when talking about Geometry/Graphs.	”The graph crosses at the x-intercept $(2, 0)$.”

Factor vs. Divisor

Term	Meaning
Factor	A math piece that divides in perfectly, leaving a remainder of 0.
Divisor	The piece you are attempting to divide by. It might be a factor, or it might leave a messy remainder.

Factor Theorem vs. Remainder Theorem

Theorem	What it tells you
Remainder Theorem	If you plug $c$ into an equation, the answer IS the remainder.
Factor Theorem	If the Remainder Theorem gives you exactly $0$, then $(x-c)$ is a perfect factor.

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Frequently Asked Questions