Question

factorise : x^3 - 2x^2 - x + 2​

Answer 1

hey there here is the answer

hope this helps u ^_^

Answer 2

TO FACTORISE :-

${x}^{3} - 2 {x}^{2} - x + 2$

SOLUTION :-

We can easily factorise it by using Factor Theorem.

By applying factor theorem 1 is the zero of the polynomial so,

${x}^{3} - 2 {x}^{2} - x + 2 \\ \\ = 1 - 2 - 1 + 2 \\ \\ = 0$

Hence, x - 1 is a factor of p(x)

We can divide it with p(x) to get the factor and remainder zero by using factor Theorem.

Now after dividing we got a quadratic factor which can be factorise again by middle term factorisation.

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

HENCE, THE CUBIC POLYNOMIAL IS FACTORISED.