# How do you factor 2x^2 + 14x - 16?

Sep 28, 2015

$2 {x}^{2} + 14 x - 16 = \left(2 x - 2\right) \left(x + 8\right)$

#### Explanation:

First you factorise the entire polynomial by 2
$2 \left({x}^{2} + 7 x - 8\right)$

Then, you would like to find two numbers that add together to give $+ 7$ and multiply together to give $- 8$.

You will find these two numbers are +8 and -1.

Use that information to factorise the expression.
$2 \left(x - 1\right) \left(x + 8\right)$

Finally, Multiply the 2 back into one of the brackets.

$\left(2 x - 2\right) \left(x + 8\right)$

Hope that helps

Sep 28, 2015

$2 {x}^{2} + 14 x - 16 = \textcolor{red}{2 \left(x - 1\right) \left(x + 8\right)}$

#### Explanation:

$2 {x}^{2} + 14 x - 16$

Factor out the GCF $2$.

$2 \left({x}^{2} + 7 x - 8\right)$

Factor $\left({x}^{2} + 7 x - 8\right)$.

Find two numbers that when added equal $7$ and when multiplied equal $- 8$. The numbers $- 1$ and $8$ fit the criteria.

(x^2+7x-8)=color(red)((x-1)color(red)((x+8)

$2 {x}^{2} + 14 x - 16 = \textcolor{red}{2 \left(x - 1\right) \left(x + 8\right)}$