if $x^{2}+mx + m$ is a perfect - square trinomial, which equation must be true?\n$x^{2}+mx + m=(x…

if $x^{2}+mx + m$ is a perfect - square trinomial, which equation must be true?\n$x^{2}+mx + m=(x - 1)^{2}$\n$x^{2}+mx + m=(x + 1)^{2}$\n$x^{2}+mx + m=(x + 2)^{2}$\n$x^{2}+mx + m=(x + 4)^{2}$

if $x^{2}+mx + m$ is a perfect - square trinomial, which equation must be true?\n$x^{2}+mx + m=(x - 1)^{2}$\n$x^{2}+mx + m=(x + 1)^{2}$\n$x^{2}+mx + m=(x + 2)^{2}$\n$x^{2}+mx + m=(x + 4)^{2}$

Answer

Explanation:

Step1: Expand perfect - square formulas

The general form of a perfect - square trinomial is $(a + b)^2=a^{2}+2ab + b^{2}$. For $(x - 1)^2=x^{2}-2x + 1$, here $m=-2$ and $m = 1$, not consistent. For $(x + 1)^2=x^{2}+2x+1$, here $m = 2$ and $m = 1$, not consistent. For $(x + 2)^2=x^{2}+4x + 4$, here $m = 4$ and $m = 4$, consistent. For $(x + 4)^2=x^{2}+8x+16$, here $m = 8$ and $m = 16$, not consistent.

Answer:

$x^{2}+mx + m=(x + 2)^2$