I need to factor this trinomial
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
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).