Polynomial Vocabulary

An expression that can be written in the form shown in the image where all the coefficients are real numbers and all the exponents are positive integers.

greatest degree (exponent) of all the monomials

degree of 0 (example: 7)

degree of 1 (example: 2x)

degree of 2 (example: -3x²+2)

degree of 3 (example: -4x³-2x)

degree of 4 (example: x⁴+2x)

polynomial with one term

polynomial with three terms

a polynomial whose terms are ordered by degree from greatest to least

a polynomial expression written as a product of factors. Example: 2x(2x-3)(x+5)

polynomial with two terms

Performing the operation on two members of the set produces another member of the set.

A number that includes a i, which is the square root of -1

The expression with the largest number and highest degree that can be divided evenly into each term of an expression

Factoring by pulling out the GCF of groups of terms

Factoring by substituting an expression with a "u" so that the expression becomes quadratic

A point at which the polynomial function values change from increasing to decreasing or decreasing to increasing.

A y-value that is smaller than the values for all other y-values in some neighborhood in the domain of a function.

A y-value that is larger than the values for all other y-values in some neighborhood in the domain of a function.

x²-y² = (x+y)(x-y)

x²±y² = x²+2xy+y²

a³-b³=(a-b)(a²+ab+b²)

a³ + b³ = (a + b)(a² - ab + b²)

A method of expanding the expression (x+y)ⁿ for any whole number, n.

the number of times that a factor is repeated in the factorization of a polynomial expression

A polynomial, P(x), of degree n≥1 has exactly n total complex roots (repeated roots counted separately)

States a constraint on rational solutions of a polynomial equation. The theorem states that each rational solution x = p/q, written in lowest terms so that p and q are relatively prime, satisfies: p is an integer factor of the constant term a0, and q is an integer factor of the leading coefficient an.

if the polynomial expression that defines the function P is divided by x-a then the remainder is the number P(a)

c is a zero of polynomial P(x) if and only if x-c is a factor of P(x).

describes the values of a function at the positive and negative extremes in its domain

If f is a polynomial of degree n, then f has at most n-1 turning points. Conversely, If the graph of a polynomial function has n-1 turning points, then the function has a degree of n or more.

A function of the form f(x) = axⁿ , where n is a real number.

If f is continuous on the closed interval [a,b] and k is between f(a) and f(b), then there exists a number c between a and b for which f(c) = k. (Note that this is an existence theorem.)