#### Answer

$2(x+7)^2$

#### Work Step by Step

Factoring the $GCF=2$, then the given expression, $
2x^2+28x+98
$, is equivalent to
\begin{array}{l}
2(x^2+14x+49)
.\end{array}
The two numbers whose product is $ac=
1(49)=49
$ and whose sum is $b=
14
$ are $\{
7,7
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
2(x^2+14x+49)
$, is
\begin{array}{l}\require{cancel}
2(x^2+7x+7x+49)
\\\\=
2[(x^2+7x)+(7x+49)]
\\\\=
2[x(x+7)+7(x+7)]
\\\\=
2[(x+7)(x+7)]
\\\\=
2(x+7)^2
.\end{array}