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

User Tankthinks
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2 Answers

4 votes

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

User TechnoIndifferent
by
8.5k points
2 votes
you divide 8 by 2 the square it so it would be 4 squared which equals 16
User Pitermarx
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7.9k points

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