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Math 102 4.1 "Dividing Polynomials" Objectives: * Divide a polynomial by a binomial divisor. * Use synthetic division to determine the quotient and remainder for division problems. Dividing a Polynomial by a Binomial Divisor Division Algorithm for Polynomials: If f (x) and g (x) are polynomials and g (x) 6= 0; then unique polynomials q (x) and r (x) exist such that where r (x) = 0 or the degree of r (x) is less than the degree of g (x) : Example 1: (Dividing polynomials using the division algorithm) Find the quotient and remainder for each division problem. a) 20x2 c) 8y 3 39x + 18 y2 y+5 (5x 6) y2 + y b) x5 d) 3x2 Page: 1 1 (x + 1) 2xy 9y 2 (x 2y) Notes by Bibiana Lopez College Algebra by Kaufmann and Schwitters 4.1 Synthetic Division Example 2: (Dividing polynomials using synthetic division) Use synthetic division to determine the quotient and remainder for each division problem. a) 2x2 5x c) 4x4 5x2 + 1 3 (x x 3) b) 4x2 + 5x 1 2 c) 2x3 + 3x2 Page: 2 4 (x + 2) 2x + 3 x+ 1 2 Notes by Bibiana Lopez