Question

factorise x3-2x2-5x+6​

Answer 1

Step-by-step explanation:

Given :-

x^3-2x^2-5x+6

To find:-

Factorise x^3-2x^2-5x+6?

Solution:-

Given expression is x^3-2x^2-5x+6

It can be written as

x^3-3x^2+x^2-3x-2x+6

It can be arranged as

=> (x^3-3x^2)+(x^2-3x)-(2x-6)

=> x^2(x-3) +x(x-3) -2(x-3)

=> (x-3)(x^2+x-2)

=> (x-3)(x^2-x+2x-2)

=>(x-3)[x(x-1)+2(x-1)]

=> (x-3)(x-1)(x+2)

x^3-2x^2-5x+6 = (x-3)(x-1)(x+2)

Answer:-

Factorization of the given expression x^3-2x^2-5x+6 is (x-3)(x-1)(x+2)

Check:-

(x-3)(x-1)(x+2)

=> [(x-3)(x-1)](x+2)

=> (x^2-x-3x+3)(x+2)

=>(x^2-4x+3)(x+2)

=>x^3-4x^2+3x+2x^2-8x+6

=>x^3-2x^2-5x+6

Verified the given relation.