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

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Answer 1 · 2018-06-22T20:32:20

$2 x$ $2x$

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 $x$ $x$ term.

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

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

Let's look at the $x$ $x$ terms: $x^{2}, x, x^{3}$ $x^2, x, x^3$

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

Hence, the GCF is $2 x$ $2x$ .

You would factor as

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

How do you find the greatest common factor of 18x^2+16x-12x^318x2+16x−12x3 18x^2+16x-12x^3?