# Is it possible to factor #y= 3x^3+8x^2+3x-2 #? If so, what are the factors?

##### 1 Answer

Feb 12, 2016

#3x^3+8x^2+3x-2 = (x+1)(3x-1)(x+2)#

#### Explanation:

Let

First notice that

#y = 3x^3+8x^2+3x-2 = (x+1)(3x^2+5x-2)#

We can factor the remaining quadratic by grouping, with the help of an AC Method.

Look for a pair of factors of

#3x^2+5x-2#

#=3x^2+6x-x-2#

#=(3x^2+6x)-(x+2)#

#=3x(x+2)-1(x+2)#

#=(3x-1)(x+2)#

Putting it all together:

#3x^3+8x^2+3x-2 = (x+1)(3x-1)(x+2)#