Answer
$(3k-5q)(4k+q)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
12k^2-17kq-5q^2
,$ use the factoring of trinomials in the form $ax^2+bx+c.$
$\bf{\text{Solution Details:}}$
In the trinomial expression above, $a=
12
,b=
-17
,\text{ and } c=
-5
.$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac=
12(-5)=-60
$ and whose sum is $b$ are $\left\{
-20,3
\right\}.$ Using these two numbers to decompose the middle term results to
\begin{array}{l}\require{cancel}
12k^2-20kq+3kq-5q^2
.\end{array}
Using factoring by grouping, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(12k^2-20kq)+(3kq-5q^2)
\\\\=
4k(3k-5q)+q(3k-5q)
\\\\=
(3k-5q)(4k+q)
.\end{array}
