SOLUTION: 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

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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