When factoring polynomials, the first step is always to look at for usual factors and also to factor them out. After that, you can see if the polynomial have the right to be factored further.

You are watching: Which of the following is a requirement for a trinomial to be factored as a perfect square?

There is a special case called the difference of two squares that has a one-of-a-kind pattern for factoring.Here is the pattern:
First, notice that there space three requirements that must be met in order for us to be able to use this pattern.
1)It have to be a binomial (have 2 terms)2)Both terms have to be perfect squares (meaning the you might take the square root and also they would come out evenly.)3)There should be a subtraction/negative authorize (not addition) in in between them
If these three needs are met, then us can easily factor the binomial using the pattern. Simply...
1)Write two parenthesis2)Put a
in one and a
in the othe3)Take the square source of the first term and also put the in the prior of each parenthesis4)Take the square root of the critical term and put that in the back of each parenthesis
As before, friend can inspect your job-related by multiplying out your answer and making certain the result matches the original.
First check for usual factors - there are none, so we have the right to
continue top top to check the criteria. The is a binomial through two perfect squares and also subtraction, therefore we deserve to use this pattern.
We set up 2 parenthesis v a+ in one and a- in the various other We take the square root of x2,which is x, and put that in the
front of every parenthesis. Us take the square source of 25 i m sorry is 5 and put the in the back of each.

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Final answer: . Us can examine this by multiply it out (remember to
distribute or usage FOIL). We obtain
. This matches the original, therefore we recognize we factored correctly.
First check for typical factors – there are none, so we can
We collection up 2 parenthesis with a+ in one and a- in the various other
We take the square source of
, i beg your pardon is
, and also put the