Answer
$(2z-k)(7z+2k)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
14z^2-3zk-2k^2
,$ use the factoring of trinomials in the form $ax^2+bx+c.$
$\bf{\text{Solution Details:}}$
In the trinomial expression above, $a=
14
,b=
-3
,\text{ and } c=
-2
.$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac=
14(-2)=-28
$ and whose sum is $b$ are $\left\{
-7,4
\right\}.$ Using these two numbers to decompose the middle term results to
\begin{array}{l}\require{cancel}
14z^2-7zk+4zk-2k^2
.\end{array}
Using factoring by grouping, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(14z^2-7zk)+(4zk-2k^2)
\\\\=
7z(2z-k)+2k(2z-k)
\\\\=
(2z-k)(7z+2k)
.\end{array}