Answer
not factorable with integer coefficients
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the quadratic expression $ax^2+bx+c,$ find two numbers whose product is $ac$ and whose sum is $b$. Use these $2$ numbers to decompose the middle term of the quadratic expression and then use factoring by grouping.
$\bf{\text{Solution Details:}}$
In the given expression, $
15p^2+24pq+8q^2
,$ the value of $ac$ is $
15(8)=120
$ and the value of $b$ is $
24
.$
The possible pairs of integers whose product is $ac$ are
\begin{array}{l}\require{cancel}
\{1,120\}, \{2,60\}, \{3,40\}, \{4,30\}, \{5,24\}, \{6,20\}, \{8,15\}, \{10,12\},
\{-1,-120\}, \{-2,-60\}, \{-3,-40\}, \{-4,-30\}, \{-5,-24\}, \{-6,-20\}, \{-8,-15\}, \{-10,-12\}
.\end{array}
None of these pairs give a sum of $b$. Hence, the given expression is $\text{
not factorable with integer coefficients
.}$
