Question

Factor completely 4x4 − 24x3 + 36x2.

4x2(x − 3)2
4(x − 3)2
4x2(x + 3)(x − 3)
4x(x2 − 6x + 9)

Answer 1

factor out 4x² from everybody
4x²(x²-6x+9)
factor inner
what 2 numbers multipliy to gete 9 and add to get -6
-3 and -3
4x²(x-3)(x-3)
or
4x²(x-3)²


first option

Answer 2

The correct option is 1.

Explanation:

The given expression is

`4x^4-24x^3+36x^2`

Taking out the greatest common factor.

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

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

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

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

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

The complete factor form of the given expression is
`4x^2(x-3)^2`.

Therefore the correct option is 1.