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

1 Answer
May 3, 2018

Answer:

#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!