Factorize
x³—2x²—x+2

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Solution

x³—2x²—x+2 = $x^{2} (x - 2) - 1 (x - 2)$ Factorize by grouping
= $(x^{2} - 1) (x - 2)$ Use difference of squares formula to factorize
= (x-1)(x+1)(x-2)

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Similar questions

$(x + 1)$ is a factor of the polynomial
(a) $x^{3} - 2 x^{2} + x + 2$ (b) $x^{3} + 2 x^{2} + x - 2$
(c) $x^{3} + 2 x^{2} - x - 2$ (d) $x^{3} + 2 x^{2} - x + 2$

Q. Factorise :
1.

2 x^{2} - x - 3

- 2 x^{2} + 3 x + 9

\int (2 x + 1) \sqrt{x^{2} + x + 1} d x

will be equal to -

{(2 x^{2} + 3 x + 5)}^{1 / 2} + {(2 x^{2} + 3 x + 20)}^{1 / 2} = 15

therefore x is

Q. x³ − 2x² − x + 2

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Factorize x³—2x²—x+2

x³—2x²—x+2 = x2(x−2)−1(x−2) Factorize by grouping = (x2−1)(x−2) Use difference of squares formula to factorize = (x-1)(x+1)(x-2)

Factorize
x³—2x²—x+2

x³—2x²—x+2 = $x^{2} (x - 2) - 1 (x - 2)$ Factorize by grouping
= $(x^{2} - 1) (x - 2)$ Use difference of squares formula to factorize
= (x-1)(x+1)(x-2)