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Question 631467: completely factor the expression 4q^2+27r^4
a. 31q^2+27r^4
b. 27r^4(4q^2+1)
c. 4q(q+27r)
d. prime
If you could please explain I would really appreciate it
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! There are no common factors between the coefficients 4 and 27. There are also no common factors between the variables q^2 and r^4
So the GCF is 1. This means that it's trivial to factor out the GCF (since we get the same thing really after we do)
Also, this is a binomial. This means that only the difference of squares rule is used to factor, but we have a sum (and not a difference) of terms.
So we can't use that method either.
So this expression is prime since it can't be factored.
Note: you can also go through the other options and rule them out. For example, choice C) is 4q(q+27r) which distributes to 4q^2 + 108rq, which is NOT the original expression. So choice C is out. You would do the same for the other answer choices.
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