Question

x^3+2x^2-x-2 using factor method factorise each of the following polynomial​

Answer 1

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Question:-

x^3+2x^2-x-2 using factor method factorise each of the following polynomial

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Solution:-

(x-1)(x+1)(x-2)

Explanation:-

x^3-2x^2-x+2

=x^3-x-2x^2+2

Grouping the 1^(st 2 terms together and the 2^(nd 2 together)

=x(x^2-1)-2(x^2-1)

=(x^2-1)(x-2)

Using the identity: a^2-b^2=(a+b)(a-b)

=(x^2-1^2)(x-2)

=(x-1)(x+1)(x-2)

. 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^3-2x^2-x+2

When replacing 1,

=1^3-2xx1^2-1+2.

=>cancel1-cancel2-cancel1+cancelled

=>0

So, we get (x-1) as factor.

Then by long division, divide (x-1) by (x^3-2x^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-2x-2]

=>(x-1)[x(x+1)-2(x+1)]

=>(x-1)(x+1)(x-2)

~Hope this helps! :)