How do you find the greatest common factor of # 18x^2+16x-12x^3#?

1 Answer
Jun 22, 2018

Answer:

#2x#

Explanation:

The greatest common factor is the largest factor that evenly divides all terms in the polynomial.

There are two pieces to it in this case. First, there is a constant term. Second, there is an #x# term.

Let's look at the constants: #18, 16, 12#

The largest number that divides each of these evenly is #2#. So #2# is part of the greatest common factor.

Let's look at the #x# terms: #x^2, x, x^3#

The largest power of #x# that divides each of these evenly is #1#. So #x# is the variable part of the greatest common factor.

Hence, the GCF is #2x#.

You would factor as

#18x^2+16x-12x^3 = 2x(9x+8-6x^2)#