7.3 Products and Factors of Polynomials

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Presentation transcript:

7.3 Products and Factors of Polynomials Objectives Multiply polynomials, and divide one polynomial by another by using long division and synthetic division. Use the Remainder and Factor Theorems to solve problems.

Glossary Terms Factor Theorem long division Remainder Theorem 7.3 Products and Factors of Polynomials Glossary Terms Factor Theorem long division Remainder Theorem synthetic division

Rules and Properties a3 + b3 = (a + b)(a2 – ab + b2) 7.3 Products and Factors of Polynomials Rules and Properties Factoring the Sum and Difference of Two Cubes a3 + b3 = (a + b)(a2 – ab + b2) a3 – b3 = (a – b)(a2 + ab + b2)

x + 3 is a factor because the remainder is 0. 7.3 Products and Factors of Polynomials Key Skills Use long division to find factors and remainders of polynomials. x2 + 3x + 2 Is x + 3 a factor of x3 + 6x2 + 11x + 6? x + 3 x3 + 6x2 + 11x + 6 x3 + 3x2 3x2 + 11x 3x2 + 9x x + 3 is a factor because the remainder is 0. 2x + 6 2x + 6

7.3 Products and Factors of Polynomials Key Skills Use synthetic division to find factors and remainders of polynomials. Is x – 3 a factor of x3 – 3x2 + x + 6? 3 1 –3 1 6 3 3 x – 3 is not a factor by the Remainder Theorem (because the remainder is 9). 1 1 9 TOC