Factoring

The process of writing a number or exponent as a product.

Factorization

Any combination of factors multiplied together resulting in the product

Factors

Any set of the numbers or expressions that form a product

Prime factorization

The unique factorization of a natural number written as a product of primes

Greatest common factor GCF

Product of all the common prime factors

Relatively prime

Expressions that share no common factors other then one

GCF of monomials

Product of the GCF of the coefficient and all common variables

Factoring a polynomial

The process of rewriting a polynomial as a product of polynomial factors.

Factoring out the GCF

The process of rewriting a polynomial as a product using the GCF of all of its terms.

GCF of a polynomial

The greatest common factor of all the terms of the polynomial.

Prime polynomial

A polynomial with integer coefficients that cannot be factored as a product of polynomials with integer coefficients other than 1 and itself.

Factor by grouping

A technique for factoring polynomials with four terms

Root

A solution to a quadratic equation in standard form

Double root

A root that is repeated twice

Area of rectangle

A = lw, where l represents the length and w represents the width.

Area of square

A = s2, where s represents the length of each side.

Area of triangle

A=1/2

bh, where b represents the length of the base and h represents the height.

bh, where b represents the length of the base and h represents the height.

Area of circle

A = πr2, where r represents the radius and the constant π ≈ 3.14.

Exponential form

An equivalent expression written using a rational exponent.

Product rule for exponents

xm ⋅ xn = xm+n; the product of two expressions with the same base can be simplified by adding the exponents

Quotient rule for exponents

The quotient of two expressions with the same base can be simplified by subtracting the exponents

Power rule for exponents

(xm)n = xmn; a power raised to a power can be simplified by multiplying the exponents.

Power rule for a product

(xy)n = xnyn; if a product is raised to a power, then apply that power to each factor in the product.

FOIL

When multiplying binomials we apply the distributive property multiple times in such a way as to multiply the first terms, outer terms, inner terms, and last terms.

Check by evaluating

We can be fairly certain that we have multiplied the polynomials correctly if we check that a few values evaluate to the same results in the original expression and in the answer.

Square Root

The number that, when multiplied by itself, yields the original number.

Principle Square Root

The positive square root of a real number, denoted with the symbol √.

Radicand

The expression a within a radical sign, an.

Cube Root

The number that, when used as a factor with itself three times, yields the original number; it is denoted with the symbol 3.

Index

The positive integer n in the notation n that is used to indicate an nth root.

N th Root

The number that, when raised to the nth power, yields the original number.

Radical

Used when referring to an expression of the form an .

Principle n th Root

The positive nth root when n is even.

Product Rules for Radicals

a⋅bn=an⋅bn, where a and b represent positive real numbers.

Quotinct Rules for Radicals

a

b

n=

an

bn

, where a and b represent positive real numbers.

b

n=

an

bn

, where a and b represent positive real numbers.

Simplified Radicals

A radical where the radicand does not consist of any factor that can be written as a perfect power of the index.

Radical Expression

An algebraic expression that contains radicals.

Square Root Function

The function f(x)=(square root)x

Cube root function

The function f(x)=x3.

Like Radicals

Radicals that share the same index and radicand.

Similar Radicals

Term used when referring to like radicals.

Conjugates

The factors (a + b) and (a − b) are conjugates.

Rationalizing the Denominator

The process of determining an equivalent radical expression with a rational denominator.

Rational Exponents

The fractional exponent m/nthat indicates a radical with index n and exponent m:

am/n=amn.

Exponential Form

An equivalent expression written using a rational exponent.

Radical Equation

Any equation that contains one or more radicals with a variable in the radicand.

Squaring Property of Equality

Given real numbers a and b, where a = b, then a2 = b2.

Extraneous Solution

A solution that does not solve the original equation.

Power Property of Equality

Given any positive integer n and real numbers a and b, where a=b,then an=bn

Root

A solution to a quadratic equation in standard form.