If x2 + mx + m is a perfect-square trinomial, which equation must be true? x2 + mx + m = (x - 1) 2 x2 + mx + m = (x + 1) 2 x2 + mx + m = (x + 2) 2 x2 + mx + m = (x + 4) 2

The correct answer is x ² + mx+m = (x+2) ².

Explanation:

A perfect square trinomial can be factored into something of the form (x+m) ². When we multiply this square back through, we have

(x+m) (x+m) = x*x+m*x+x*m+m*m=x ² + 2mx+m ².

Since we know this equals x ² + mx+m, this tells us that 2m=m ². Using this equation, divide both sides by m:

2m/m = m ² / m

2=m.

This means that (x+m) ² = (x+2) ².