Question

5. Factorise :
(i) x^3 - 2x^2 - x + 2​

Answer 1

x³ - 2x² - x + 2.

Constant term = 2

Factors of 2 = ±1, ±2.

By trial and error, we got that (1) is the zero of the polynomial given.

∴ (x - 1) is a factor.

So,

x³ - 2x² - x + 2

= x³ - x² - x² + x - 2x + 2

= x²(x - 1) - x(x - 1) -2 (x - 1)

{You can divide the polynomial by (x - 1) to get the below value too.}

= (x - 1)(x² - x - 2)

= (x - 1){x² - (2 - 1)x - 2}

= (x - 1){x² - 2x + x - 2}

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

= (x - 1)(x + 1)(x - 2) → Uttar.