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

May 3, 2018

$2 \left(x + 8\right) \left(x - 1\right)$

#### Explanation:

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

To factor, we have to find the GCF, or Greatest Common Factor. This means the largest factor that all expressions have.

Therefore, the GCF is $2$. So when we factor it becomes:
$2 \left({b}^{2} + 7 b - 8\right)$.

We can still factor ${b}^{2} + 7 b - 8$ further.
This expression is in standard form, or $a {x}^{2} + b x + c$
When we factor trinomials, we need two numbers that:

• Add up to $b$ (in this case, that means $7$)
• Multiply up to $a \cdot c$ (in this case, that means $1 \cdot - 8 = - 8$)

Those two numbers are $8$ and $- 1$, as shown here:

• $8 - 1 = 7$
• $8 \cdot - 1 = - 8$

Now, we put it in factored form:
$\left(x + 8\right) \left(x - 1\right)$

Adding on with the earlier factored out $2$, the final answer is:
$2 \left(x + 8\right) \left(x - 1\right)$

Hope this helps!