#### Answer

$7x \left( 3x+5 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
21x^2+35x
,$ get the $GCF.$ Then, divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient.
$\bf{\text{Solution Details:}}$
The $GCF$ of the constants of the terms $\{
21,35
\}$ is $
7
$ since it is the highest number that can divide all the given constants. The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{
x^2,x
\}$ is $
x
.$ Hence, the entire expression has $GCF=
7x
.$
Factoring the $GCF=
7x
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
7x \left( \dfrac{21x^2}{7x}+\dfrac{35x}{7x}
\right)
\\\\=
7x \left( 3x+5 \right)
.\end{array}