# Answer to Question #10663 in Abstract Algebra for Manthan khorwal

Question #10663

Factorise:

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

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

Expert's answer

& 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)

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)

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