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

4x^2 (x-3) ^2

Step-by-step explanation:

Original expression: 4x^4 - 24x^3 + 36x^2

So looking at this we see that there are a few things we have in common among all the terms in this expression

1. They all have at least a value of x^2

2. They are all multiples of 4

Knowing this we can begin to factor and pull out an x^2 term

x^2 (4x^2 - 24x + 36)

Then we can factor out the 4

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

Now we have reached a quadratic, and in this case we can also factor this quadratic:

We need a number that when multiplied will give positive nine and add to - 6 so we can do - 3 and - 3 to fix these specifications:

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

Answer: 4x^2 (x-3) ^2 the will be the answer if you factor it