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: 32

Answer

$(x-11)(x+9)$

Work Step by Step

In decreasing order of exponents, the given expression, $ -2x-99+x^2 ,$ is equivalent to \begin{array}{l} x^2-2x-99 .\end{array} The 2 numbers whose product is $ac= 1(-99)=-99 $ and whose sum is $b= -2 $ are $\left\{ -11,9 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} x^2-11x+9x-99 \\\\= (x^2-11x)+(9x-99) \\\\= x(x-11)+9(x-11) \\\\= (x-11)(x+9) .\end{array}
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