Question #10635

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

Expert's answer

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)

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)

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