Question

Factor completely: 4x^4 - 24x^3 + 36x^2.

A) 4x^2(x - 3)^2
B) 4(x - 3)^2
C) 4x^2(x^2 - 6x + 9)
D) 4x(x^2 - 6x + 9)

Answer 1

The given expression can be completely factored to 4x^2(x^2 - 6x + 9).

Step-by-step explanation:

To factor the given expression completely, we start by factoring out the greatest common factor. In this case, the greatest common factor is 4x^2, so we can factor it out:

4x^4 - 24x^3 + 36x^2 = 4x^2(x^2 - 6x + 9)

We cannot factor the expression x^2 - 6x + 9 any further, so the completely factored form of the original expression is:

Option C) 4x^2(x^2 - 6x + 9)