Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-4 Factoring Quadratic Expressions - Practice and Problem-Solving Exercises - Page 222: 86

Answer

$(x-9)(x-10)$

Work Step by Step

Let $z= (x-2) .$ The given expression, $ (x-2)^2-15(x-2)+56 ,$ is equivalent to \begin{align*} z^2-15z+56 .\end{align*} Using the factoring of trinomials in the form $x^2+bx+c,$ the expression above has $c= 56 $ and $b= -15 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ -7,-8 \right\}.$ Using these two numbers, the factored form of the expression above is \begin{align*} (z-7)(z-8) .\end{align*} Substituting back $z= (x-2),$ the expression above is equivalent to \begin{align*} & (x-2-7)(x-2-8) \\&= (x-9)(x-10) .\end{align*}
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