# How do you factor x^3+2x^2+14x+7x^2?

Mar 20, 2017

See the entire solution process below:

#### Explanation:

First, group and combine like terms:

${x}^{3} + 2 {x}^{2} + 7 {x}^{2} + 14 x \to$

${x}^{3} = \left(2 + 7\right) {x}^{2} + 14 x$

${x}^{3} + 9 {x}^{2} + 14 x$

Next, factor out an $x$ from each term in the expression:

$\left(x \cdot {x}^{2}\right) + \left(x \cdot 9 x\right) + \left(x \cdot 14\right) \to$

$x \left({x}^{2} + 9 x + 14\right)$

Because $7 + 2 = 9$ and $7 \cdot 2 = 14$ we can factor the quadratic term as:

$x \left(x + 7\right) \left(x + 2\right)$

Mar 20, 2017

$x \left(x + 2\right) \left(x + 7\right)$

#### Explanation:

${x}^{3} + 2 {x}^{2} + 14 x + 7 {x}^{2}$

$\therefore = {x}^{3} + 2 {x}^{2} + 7 {x}^{2} + 14 x$

$\therefore = {x}^{3} + 9 {x}^{2} + 14 x$

$\therefore = x \left({x}^{2} + 9 x + 14\right)$

$\therefore = x \left(x + 2\right) \left(x + 7\right)$