Question

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

Answer 1

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!