Answer to Question #10635 in Algebra for Manthankhorwal

Question

Factorise:

1. 3x3-2x2-7x-2
2. x3+5x2-4x-20
3. 2x3-x2-13x-6
4.2x3+7x2+x-10

Answer 1

Use factor theorem to solve these examples. At first you need to find roots of given polynomial. Let's consider
2. x3+5x2-4x-20
x3+5x2-4x-20=0
Substituting x=2 we find out that it's a root. So we need to divide x3+5x2-4x-20 by x-2
We obtain x^2+7x+10
Therefore x3+5x2-4x-20=(x-2)(x^2+7x+10)
Let's factorise x^2+7x+10
x^2+7x+10=0
x=-5, x=-2
So x^2+7x+10=(x+5)(x+2)
Finally we get
x3+5x2-4x-20=(x-2)(x+5)(x+2)