Answer to Question #10663 in Abstract Algebra for Manthan khorwal

Question

Factorise:
1. 3x3-2x2-7x-2

Answer 1

& 1. 3x3-2x2-7x-2
By substituting x=-1 we find out that it's a root. So we divide& 3x3-2x2-7x-2 by x+1
We obtain 3x2-5x-2
Therefore 3x3-2x2-7x-2=(x+1)(3x2-5x-2)
Let's find roots of 3x2-5x-2
D=25+2*4*3=25+24=49
x=(5+7)/6=2
x=(5-7)/6=-1/3
Finally we get
3x3-2x2-7x-2=3(x+1)(x-2)(x+1/3)