Answer
$(3m^2-5)(7m^2+1)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
21m^4-32m^2-5
,$ use the factoring of trinomials in the form $ax^2+bx+c.$
$\bf{\text{Solution Details:}}$
In the trinomial expression above, $a=
21
,b=
-32
,\text{ and } c=
-5
.$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac=
21(-5)=-105
$ and whose sum is $b$ are $\left\{
-35,3
\right\}.$ Using these two numbers to decompose the middle term results to
\begin{array}{l}\require{cancel}
21m^4-35m^2+3m^2-5
.\end{array}
Using factoring by grouping, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(21m^4-35m^2)+(3m^2-5)
\\\\=
7m^2(3m^2-5)+(3m^2-5)
\\\\=
(3m^2-5)(7m^2+1)
.\end{array}