Stitz-Zeager_College_Algebra_e-book

Based on the graph none of our rational zeros will

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Unformatted text preview: itute for working through it yourself. Example 3.2.1. Use synthetic division to perform the following polynomial divisions. Find the quotient and the remainder polynomials, then write the dividend, quotient and remainder in the form given in Theorem 3.4. 5 You’ll need to use good old-fashioned polynomial long division for divisors of degree larger than 1. 3.2 The Factor Theorem and The Remainder Theorem 1. 5x3 − 2x2 + 1 ÷ (x − 3) 3. 2. x3 + 8 ÷ (x + 2) 201 4 − 8x − 12x2 2x − 3 Solution. 1. When setting up the synthetic division tableau, we need to enter 0 for the coefficient of x in the dividend. Doing so gives 3 5 −2 0 ↓ 15 39 5 13 39 1 117 118 Since the dividend was a third degree polynomial, the quotient is a quadratic polynomial with coefficients 5, 13 and 39. Our quotient is q (x) = 5x2 + 13x + 39 and the remainder is r(x) = 118. According to Theorem 3.4, we have 5x3 − 2x2 +1 = (x − 3) 5x2 + 13x + 39 + 118. 2. For this division, we rewrite x + 2 as x − (−2) and pro...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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