Question

Hello can someone help me solve this question? Change it to factored form! Thank you.

Answer 1

The answer is 4(x-2)(x-2) or 4
`(x-2)^2`

Explanation:

`4x^2`-16x+16

There is a common factor of 4. Factor 4 out.

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

Now, there is no factor in front of x, so seperate the equation into two parts, with one x on both sides:

(x ____) (x____)

The constant (4) is positive. Ways to multiply to get positive numbers:

negative x negative or

positive x positive.

Since (-4x) is negative, try with negative numbers first.

(x- ___ ) (x- ___)

Factors of 4 = 1,2,2,4

4 and 1 would combine to give 5.

2 and 2, however, work!

(x-2)(x-2)

FOIL.

x^2-2x-2x+4

x^2-4x+4

The answer is 4(x-2)(x-2) or 4
`(x-2)^2`

Answer 2

4(x-2)^2

Explanation:

4x^2 -16x + 16

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

= 4(x - 2)^2 because a^2 - 2ab + b^2 = (a - b)^2