Question

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

3x
3x2
6x2
6x4

Answer 1

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.

Answer 2

`3x^2`

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`