Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set - Page 303: 35



Work Step by Step

Let $z=x^2$. Then the given expression, $ x^4+x^2-6 $, is equivalent to $ z^2+z-6 $. The two numbers whose product is $ac= 1(-6)=-6 $ and whose sum is $b= 1 $ are $\{ 3,-2 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ z^2+z-6 $, is \begin{array}{l}\require{cancel} z^2+3z-2z-6 \\\\= (z^2+3z)-(2z+6) \\\\= z(z+3)-2(z+3) \\\\= (z+3)(z-2) .\end{array} Since $z=x^2$, then the factored form of the original expression is $ (x^2+3)(x^2-2) $.
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