Factor the trinomial completely. 2a^3+16a^2+30a

Question

 

Select the correct choice below.

(a) 2a^3+16a^2+30a=?

(b) The trinomial is prime.

 

Answer 1

2a³ + 16a² + 30a CAN be factored

First, find the greatest common factor (GCF) in each of the terms:

The GCF is 2a; therefore:
= 2a (a² + 8a + 15)

Now, you are left with a quadratic equation to factor in a (a+n)(a+r) fashion:

It helps to first find the factors of 15: 1, 3, 5, 15

3+5=8; so, 3 and 5 will be the numbers for n and r

= 2a (a + 3) (a + 5)