# College Algebra 3

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
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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.
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 √.
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.
Used when referring to an expression of the form an .
Principle n th Root
The positive nth root when n is even.
a⋅bn=an⋅bn, where a and b represent positive real numbers.
a
b
n=
an
bn
, where a and b represent positive real numbers.
A radical where the radicand does not consist of any factor that can be written as a perfect power of the index.
An algebraic expression that contains radicals.
Square Root Function
The function f(x)=(square root)x
Cube root function
The function f(x)=x3.
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.