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

Question

I need to factor this trinomial

Answer 1

The first step to factoring an expression is to look for a common factor. In this expression we can factor out a from each term to become

     a(8a²+14a+3)

Now turn our attention to factoring the expression in the parentheses above

The 8a² term could be factored (8a)(a) or (4a)(2a), the 3 can only be factored as (1)(3).

Which one will give us a 14a as the middle term?

     (8a + 1)(a + 3) = 8a² + 25a + 3     Does not work

     (8a + 3)(a + 1) = 8a² + 11a + 3     Does not work

     (4a + 1)(2a + 3) = 8a² + 14a + 3   WORKS!

So, factored completely, 8a³ + 14a² + 3a = a(4a + 1)(2a + 3).