Question

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

Answer 1

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

Answer 2

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

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

$x^2+8x+16$