Question

Factorize: x3-2x-X+2 (Using long division method only)​

Answer 1

The above method is an easy on to solve this question. For factorizing other cubic polynomials, the following method can be used:

First, by trial and error method, you can find one factor as follows:

x

3

−

2

x

2

−

x

+

2

When replacing 1,

⇒

1

3

−

2

×

1

2

−

1

+

2

⇒

1

−

2

−

1

+

2

⇒

0

So, we get

(

x

−

1

)

as factor.

Then by long division, divide

(

x

−

1

)

by

(

x

3

−

2

x

2

−

x

+

2

)

You get

⇒

(

x

−

1

)

(

x

2

−

x

−

2

)

Then you have to factorize it by splitting the middle term method.

⇒

(

x

−

1

)

[

x

2

+

x

−

2

x

−

2

]

⇒

(

x

−

1

)

[

x

(

x

+

1

)

−

2

(

x

+

1

)

]

⇒

(

x

−

1

)

(

x

+

1

)

(

x

−

2

)

~Hope this helps! :)