# Polynomial Vocabulary

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polynomial
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.
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degree of a Polynomial
greatest degree (exponent) of all the monomials
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constant
degree of 0 (example: 7)
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linear
degree of 1 (example: 2x)
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degree of 2 (example: -3x²+2)
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cubic
degree of 3 (example: -4x³-2x)
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quartic
degree of 4 (example: x⁴+2x)
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monomial
polynomial with one term
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Trinomial
polynomial with three terms
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standard Form
a polynomial whose terms are ordered by degree from greatest to least
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factored form
a polynomial expression written as a product of factors. Example: 2x(2x-3)(x+5)
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binomial
polynomial with two terms
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A Closed Set Under and Operation
Performing the operation on two members of the set produces another member of the set.
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Imaginary number
A number that includes a i, which is the square root of -1
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greatest common factor
The expression with the largest number and highest degree that can be divided evenly into each term of an expression
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Factoring by grouping
Factoring by pulling out the GCF of groups of terms
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factoring by substitution
Factoring by substituting an expression with a "u" so that the expression becomes quadratic
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turning point
A point at which the polynomial function values change from increasing to decreasing or decreasing to increasing.
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relative minimum
A y-value that is smaller than the values for all other y-values in some neighborhood in the domain of a function.
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relative maximum
A y-value that is larger than the values for all other y-values in some neighborhood in the domain of a function.
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difference of squares
x²-y² = (x+y)(x-y)
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square of a binomial
x²±y² = x²+2xy+y²
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difference of cubes
a³-b³=(a-b)(a²+ab+b²)
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sum of cubes
a³ + b³ = (a + b)(a² - ab + b²)
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binomial expansion
A method of expanding the expression (x+y)ⁿ for any whole number, n.
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multiplicity
the number of times that a factor is repeated in the factorization of a polynomial expression
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Fundamental Theorem of Algebra
A polynomial, P(x), of degree n≥1 has exactly n total complex roots (repeated roots counted separately)
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Rational Roots Theorem
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.
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Remainder Theorem
if the polynomial expression that defines the function P is divided by x-a then the remainder is the number P(a)
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Factor Theorem
c is a zero of polynomial P(x) if and only if x-c is a factor of P(x).
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end behavior