#### Answer

$2(2x-5)(x+7)$

#### Work Step by Step

The student's answer is not completely factored out since in the final answer, $2$ can still be factored from the second factor, $(2x+14).$ A simpler solution (one that involves smaller numbers) is to factor first the $GCF$ before factoring the trinomial.
The correct solution is as follows:
\begin{array}{l}\require{cancel}
4x^2+18x-70
\\\\=
2(2x^2+9x-35)
\\\\=
2(2x^2-5x+14x-35)
\\\\=
2[(2x^2-5x)+(14x-35)]
\\\\=
2[x(2x-5)+7(2x-5)]
\\\\=
2[(2x-5)(x+7)]
\\\\=
2(2x-5)(x+7)
.\end{array}