Question

Factorise:
${x}^{3} - {2x}^{2} - x + 2$
Class 9 standard...
Please solve it. ​

Answer 1

Answer:

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

Step-by-step explanation:

We have

${x}^{3} - 2 {x}^{2} - x + 2 \\ = {x}^{2}(x - 2) - (x - 2) \\ = (x - 2)( {x}^{2} - 1) \\ = (x - 2)(x - 1)(x + 1)$

So the factors are

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

Answer 2

Answer:

$\sf x^3 - 2x^2 - x + 2 = (x-2)(x-1)(x+1)$

Step-by-step explanation:

$\implies \sf x^3 - 2x^2 - x + 2$

$\implies \sf x^2 (x-2) - x + 2$

$\implies \sf x^2 (x - 2) - (x - 2)$

$\implies \sf (x - 2)(x^2 - 1)$

Use a² - b² = (a - b)(a + b)

$\implies \sf (x - 2)(x - 1)(x + 1)$

$\qquad \therefore {\boxed{\sf (x-2)(x-1)(x+1)}}$