Can the function f (x) = x²-4x+4 be factored? If so, write the factored form.

f (x) = (x - 2) ²

Step-by-step explanation:

f (x) = x² - 4x + 4 is a perfect trinomial.

You know a trinomial is perfect when double the square root of the first term multiplied by the square root of the last term equals the middle term.

As an equation, a trinomial in the form ax² + bx + c = 0:

2√a√c = b is a perfect trinomial.

Perfect trinomial are factored in this form:

(√a ± √c) (√a ± √c) = (√a ± √c) ²

Whether the sign is + or - depends on if the middle term is positive or negative.

In f (x) = x²-4x+4, the middle term is a negative.

The square root of the first term is 1.

The square root of the second term is 2.

The factored form is (x - 2) ²