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: 68

Answer

$(x^2-2)(x^2-3)$

Work Step by Step

The two numbers whose product is $ac= 1(6)=6 $ and whose sum is $b= -5 $ are $\{ -2,-3 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ x^4-5x^2+6 $, is \begin{array}{l}\require{cancel} x^4-2x^2-3x^2+6 \\\\= (x^4-2x^2)-(3x^2-6) \\\\= x^2(x^2-2)-3(x^2-2) \\\\= (x^2-2)(x^2-3) .\end{array}
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