SOLUTION: Determine whether each of the following trinomials is perfect square. If it is, factor the trinomial. Stumped x squared-24x+48

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Question 115090This question is from textbook Beginning algebra
: Determine whether each of the following trinomials is perfect square. If it is, factor the trinomial.
Stumped
x squared-24x+48 This question is from textbook Beginning algebra

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If the polynomial is a perfect square, then there is an a such that
x%5E2-24x%2B48=%28x%2Ba%29%5E2
You can expand the right hand side and match up terms.
x%5E2-24x%2B48=x%5E2%2B2ax%2Ba%5E2
You have to satisfy two terms for the equation to be a perfect square
1.-24x=2ax
2.48=a%5E2
From 1,
1.-24x=2ax
-24=2a
highlight%28a=12%29
From 2,
2.48=a%5E2
a=sqrt%2848%29
highlight%28a=6.93%29
Since you can't satisfy both requirements 1 and 2, the polynomial is not a perfect square.