Stitz-Zeager_College_Algebra_e-book

We now present other theorems and discuss how to nd

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Unformatted text preview: ecompose −12x2 − 8x + 4 into a multiple of (2x − 3) plus a constant term. Since we have found such a way, we can be sure it is the only way. The next example pulls together all of the concepts discussed in this section. 202 Polynomial Functions Example 3.2.2. Let p(x) = 2x3 − 5x + 3. 1. Find p(−2) using The Remainder Theorem. Check your answer by substitution. 2. Use the fact that x = 1 is a zero of p to factor p(x) and find all of the real zeros of p. Solution. 1. The Remainder Theorem states p(−2) is the remainder when p(x) is divided by x − (−2). We set up our synthetic division tableau below. We are careful to record the coefficient of x2 as 0, and proceed as above. −2 2 0 −5 ↓ −4 8 2 −4 3 3 −6 −3 According to the Remainder Theorem, p(−2) = −3. We can check this by direct substitution into the formula for p(x): p(−2) = 2(−2)3 − 5(−2) + 3 = −16 + 10 + 3 = −3. 2. The Factor Theorem tells us that since x = 1 is a zero of p, x − 1 is a factor of p(x). To factor p(x), we divide 1 2 0 ...
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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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