Polynomial Definitions

A term is a number or the product of a number & variables raised to powers.

The (numerical) coefficient is the numerical factor of a term.

A polynomial is a finite sum of terms of the form axn, where a is a real number and n is a whole number (0, 1, 2, …). (poly = many, nomial = name or term, so “many terms”)

A monomial is a polynomial with exactly 1 term. (mono = one)

A binomial is a polynomial with exactly 2 terms. (bi = two)

A trinomial is a polynomial with exactly 3 terms. (tri = three)

The degree of a term is the sum of the exponents of the variables in the term.

Example: the degree of 6x is 1, the degree of 3xy² is 3, and the degree of 7 is 0, since 7 = 7x⁰.

The degree of a polynomial is the greatest degree of its terms,

Example the degree of 6x + 3xy² – 7 is 3.

To evaluate a polynomial substitute the given value(s) for the corresponding variable(s). When a polynomial is a function and want to evaluate we replace the independent variable with the given value.

Examples:

• f(x) = 6x – 4, find f(3)

  f(3) = 6(3) – 4

  f(3) = 18 – 4

  f(3) = 14

• 2x3 – 3x + 4, evaluate when x = -2

  2(-2)3 – 3(-2) + 4

  2*-8 - -6 + 4

  -16 + 6 + 4

  -10 + 4

  -6