Factorise 2x^3 + 3x^2 - 3x - 2?

Question

Absolutely no clue how to do this

Answer 1

find the root. Start to plug in some number
let's try 1

2(1)^3 + 3(1)^2 - 3(1) - 2
2 + 3 - 3 - 2
0

1 is one of the root, thus, (x - 1) is one of the factor

use synthetic long division
1 l.. 2 ... 3 ... -3 ... -2
...l ... .... 2 .... 5 .... 2
-------------------------------
..... 2 ... 5 .... 2 ..... 0

you have:
(x - 1) (2x^2 + 5x + 2)

factor the rest
(x - 1) (2x^2 + 4x + 1x + 2)

(x - 1) [ (2x^2 + 4x) + (1x + 2)

(x - 1) (2x (x + 2) + 1(x + 2) ]

(x - 1) (2x + 1) (x + 2)

hope this helps