# Chapter 5 - Section 5.2 - Factoring Trinomials - 5.2 Exercises: 24

not factorable with integer coefficients

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the quadratic expression $x^2+bx+c,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$. Then, express the factored form as $(x+m_1)(x+m_2).$ $\bf{\text{Solution Details:}}$ In the given expression, $p^2-12p-27 ,$ the value of $c$ is $-27$ and the value of $b$ is $-12 .$ The possible pairs of integers whose product is $c$ are \begin{array}{l}\require{cancel} \{1,-27\}, \{3,-9\}, \{-1,27\}, \{-3,9\} .\end{array} Among these pairs, none gives a sum of $b.$ Hence, the given expression is $\text{ not factorable with integer coefficients .}$

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