Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set: 59

Answer

$(s-6t)(s+2t)$

Work Step by Step

The 2 numbers whose product is $ac= 1(-12)=-12 $ and whose sum is $b= -4 $ are $\left\{ -6,2 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $ s^2-4st-12t^2 ,$ then the factored form is \begin{array}{l} s^2-6st+2st-12t^2 \\\\= (s^2-6st)+(2st-12t^2) \\\\= s(s-6t)+2t(s-6t) \\\\= s(s-6t)+2t(s-6t) \\\\= (s-6t)(s+2t) .\end{array}
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