Question

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

Answer 1

Answer:

x^2+mx+m=(x+2)^2

Step-by-step explanation:

Answer 2

Hello!

The answer is:

The third option,

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

Why?

We are looking for an equation that establishes a relationship between the perfect-square trinomial and the givens notable products.

So, we are looking for a notable product that gives us a value of "m" that is the coefficient of the linear term (x) and it's also the constant term.

- Trying with the two first options, we have:

$(x+1)^{2}=x^{2}+2x+ 1\\\\(x-1)^{2}=x^{2}-2x+ 1$

We can see that for these first two options, the value of m has not the same value for the coefficient of the linear term and the constant term since m is equal 2 and the constant number is not 2.

- Trying with the third option, we have:

$(x+2)^{2}=x^{2}+2*(2*x)+2^{2}=x^{2} +4x+4$

Now, we can see that the value of m is the same for the coefficient of the linear term and the constant term, we can see that m is equal to 4.

So, the correct option is the third option, because

$m=4$

$x^{2} +mx+m=(x+2)^{2}=x^{2} +4x+4=x^{2} +mx+m$

Have a nice day!