Question

Which value is needed to create a perfect square trinomial from the expression x2 + 8x + _____?

Answer 1

Answer:
`x^2+8x+16`

Step-by-step explanation:

A perfect square is an expression in the form

`(x+a)^2`

which can be rewritten in a trinomial form:

`(x+a)^2 = (x+a)(x+a)=x^2 +ax+ax+a^2 = x^2 +2ax +a^2` (1)

In this problem, we have the following trinomial:

`x^2 + 8x +C` (2)

with C unknown. By comparing (1) and (2), we see that

`2a=8\\a^2 = C`

from the first equation, we find

`a=4`

and substituting into the second one, we find

`C=a^2=4^2=16`

So, the perfect square trinomial form is

`x^2+8x+16`

Answer 2

you divide 8 by 2 the square it so it would be 4 squared which equals 16