Question

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

Answer 1

`2(x+8)(x-1)`

Explanation:

`2b^2 + 14b - 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(b^2 + 7b - 8)`.

We can still factor `b^2 + 7b - 8` further.
This expression is in standard form, or `ax^2 + bx + c`
When we factor trinomials, we need two numbers that:

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

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

• `8 - 1 = 7`
• `8 * -1 = -8`

Now, we put it in factored form:
`(x + 8)(x-1)`

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

Hope this helps!