Question

Factorise

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

Answer 1

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

Explanation:

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

• Take x² common from first two terms.

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

• Take (x - 2) common from whole expression.

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

• Factorise (x² - 1) by using the identity → (a² - b²) = (a + b)(a - b)

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

Answer 2

Solution given:

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

take common from two each term

x²(x-2)-1(x-2)

take common again and keep left one on other bracket

(x-2)(x²-1) or (x-1)(x+1)(x-2) is a required answer.

note:using formula a²-b²=(a+b)(a-b) for x²-1.