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

I need to factor this trinomial

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Jason T. | Jason Tutors Math & PhysicsJason Tutors Math & Physics
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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).