Factor the trinomial completely.

Question

8a^3 + 14a^2 +3a

Select the correct choice below.

(a) 8a^3 + 14a^2 + 3a =?

(b) The polynomial is prime.

Answer 1

It looks like you have a bunch of these, so let's defer the whole factoring and prime discussion to the first one of these we solved today. With a cubic (3rd degree polynomial, highest term is something like x^3) the three best factoring methods to consider for starters are grouping, sum or difference of cubes, or simplify to the product of a monomial and quadratic and go from there.

There's an 'a' in every term, so let's simplify.

8a^3 + 14a^2 + 3a = a(8a^2 + 14a +3)

Now you can determine if the quadratic is factorable over integers. You're already a pro at that, right? If it is factorable, don't forget that 'a' in your final answer: = a(    )(   )  i.e. three factors.