Question

Which product of prime polynomials is equivalent to 8x4 + 36x3 – 72x2?

4x(2x – 3)(x2 + 6)
4x2(2x – 3)(x + 6)
2x(2x – 3)(2x2 + 6)
2x(2x + 3)(x2 – 6)

Answer 1

4x2(2x – 3)(x + 6)

Explanation:

Given expression: 8x^4 + 36x^3 - 72x^2

Step 1: Identify the greatest common factor (GCF) of the terms.

In this case, the GCF is 4x^2. We can factor it out from each term.

Step 2: Divide each term by the GCF.

Dividing each term by 4x^2, we get:

8x^4 / (4x^2) = 2x^2

36x^3 / (4x^2) = 9x

-72x^2 / (4x^2) = -18

Step 3: Rewrite the expression using the factored form.

Now that we have factored out the GCF, we can write the expression as:

8x^4 + 36x^3 - 72x^2 = 4x^2(2x^2 + 9x - 18)

The factored form is 4x^2(2x^2 + 9x - 18).

Step 4: Compare the factored form with the given options.

a. 4x(2x - 3)(x^2 + 6)

b. 4x^2(2x - 3)(x + 6)

c. 2x(2x - 3)(2x^2 + 6)

d. 2x(2x + 3)(x^2 - 6)

Among the options, the one that matches the factored form is:

b. 4x^2(2x - 3)(x + 6)

So, the correct answer is option b. 4x2(2x – 3)(x + 6)