Question

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

Answer 1

`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)`