Which of the following is the GCF of the polynomial 4x^4+12x^3−36x^2+24x?(1 point)

Question

Which of the following is the GCF of the polynomial 4x^4+12x^3−36x^2+24x?(1 point)

2x

4x

6x

4

Answer 1

To find the greatest common factor (GCF) of a polynomial, we need to find the common factors of all the terms and then identify the largest factor.

Let's factor out the common factor of the given polynomial, 4x^4 + 12x^3 - 36x^2 + 24x:

4x(x^3 + 3x^2 - 9x + 6)

Now, let's factor each term within the parentheses:

4x(x^3 + 3x^2 - 9x + 6) = 4x((x^3 + 3x^2) + (-9x + 6))

Next, we can factor out the common factors within each pair of terms:

4x(x^2(x + 3) - 3(x - 2))

Now, we can rewrite the polynomial using the factored form:

4x(x^2(x + 3) - 3(x - 2)) = 4x(x^2(x + 3) - 3(x - 2))

Thus, the GCF of the polynomial 4x^4 + 12x^3 - 36x^2 + 24x is 4x.