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

1 Answer
Shantelle
May 3, 2018

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!

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