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

Jun 22, 2018

$2 x$

#### 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 $2 x$.

You would factor as

$18 {x}^{2} + 16 x - 12 {x}^{3} = 2 x \left(9 x + 8 - 6 {x}^{2}\right)$