Lesson 11 Understanding polynomials A monomial is a

Lesson 11 Understanding polynomials

A monomial is a number, a variable, or a product of a number and one or more variables with whole number exponents. n A polynomial is a monomial or sum of monomials. n The degree of a monomial is the sum of the exponents of the variable factors. n The degree of a polynomial is the degree of its monomial with the highest degree n

Degrees ? n 5 ab 3 n -xy 3 -3 x 2 y 2+x 2 y 3 n x 3 + 4 x 2 -3 n m 4 +. 5 m + 3 m 4

Standard form A one-variable polynomial is in standard form when all like terms are combined and its terms are in descending order by degree. n Polynomial function: n f(x) = anxn + an-1 xn-1 +…+ a 1 x + a 0 n n The leading coefficient is an, the constant term is a 0, and the degree is n

Writing a polynomial in standard form n Write in standard form and identify the leading coefficient and the constant term: n x- 5 + 4 x 2 + 2 x 5 - x 2 n 5 - 2 y + 2 y 3 -5 + 4 y 3

Classifying polynomials n. Polynomials can be classified by degree and by number of terms.

n Polynomial degree n n n n -4 X+2 x 2+x-6 x 3 -3 x 4+2 x 3 -x 2 x 5 - 4 x 2 0 1 2 3 4 5 classification by degree constant linear quadratic cubic Quartic quintic # of terms 1 2 3 1 3 2 classification by # of terms monomial binomial trinomial monomial trinomial binomial

Classify each polynomial n n x 2 -9 x 3 + x -2 x 3 - 1/2 x 5 x 3 +4 x 2 -3 m 4 +. 5 m +3 m 4

Adding polynomials To add polynomials combine like terms. n (2 x 3 -3 x 2+x-5) +(5 -x 2) n n (3 x 2+7+x) +(10 x 3+2+x 2 -x) n (5 x 3 -3 x 2)-(2 x 3 -x 2+4) n (4 m 2 -3 m+2) -(m 3 -2 m+5)