Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.3 - Dividng Polynomials - 3.3 Exercises - Page 274: 61

Answer

$\frac{5\pm \sqrt {37}}{6}$

Work Step by Step

Use the Remainder and Factor Theorem: $P(-2)=3\times16+8\times8-14\times4-31\times2+6=0$ $P(3)=3\times81-8\times27-14\times9+31\times3+6=0$ This proves that $-2,3$ are zeros of P. Use synthetic division to reduce P to quadratic form as $P(x)=(x+2)(x-3)(3x^2-5x-1)$ and the other two zeros are $x=\frac{5\pm \sqrt {37}}{6}$
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