Question

What is the greatest common factor of the terms in the polynomial 12x4 + 27x3 + 6x2?

Answer 1

Answer:

$3x^2$

Step-by-step explanation:

$12x^4 + 27x^3 + 6x^2$

The coefficients of the variables are 12, 27 and 6.  The greatest common factor (GCF) of these numbers is 3.

$\implies 3(4x^4 +9x^3 + 2x^2)$

From inspection, the GCF of the variables is $x^2$

$\implies 3x^2(4x^2+9x + 2)$

Therefore, the GCF of the terms in the polynomial is $3x^2$

Answer 2

Step-by-step explanation:

We're going to be factoring:

$12 {x}^{4} + 27 {x}^{3} + 6 {x}^{2}$

We know that the GCF between 12, 27, and 6 is 3.

We also know that the GCF of x^4, x^3, and x^2 is x^2.

When factoring:

• Use both of our GCFs, 3 and x^2 (3x^2).
• Divide our coefficients by the GCF.

$3{x}^{2} (4 {x}^{2} + 9x + 2)$

We know 3x^2 is the correct option since the polynomial is factored completely.