Question

factorise
x³-2x²-x+2​

Answer 1

Basic Concept Used :-

↝ Factorisation by Regrouping Terms

↝ Sometimes it happens that there is no common term to be taken out common in the expressions then

• We have to make the suitable groups of the terms.

• Choose the common factor among these groups.

• Find the common factors and it will give the required factors.

Let's solve the problem now!!

Given expression is

$\rm :\longmapsto\: {x}^{3} - {2x}^{2} - x + 2$

$\rm :\longmapsto\: = \: ({x}^{3} - {2x}^{2}) + ( - x + 2)$

$\rm :\longmapsto\: = \: {x}^{2}(x - 2) - 1(x - 2)$

$\rm :\longmapsto\: = \: (x - 2)( {x}^{2} - 1)$

$\rm :\longmapsto\: = \: (x - 2)( {x}^{2} - {1}^{2} )$

$\rm :\longmapsto\: = \: (x - 2)(x - 1)(x + 1)$

$\: \: \: \: \: \: \: \boxed{ \because \: { \red{ \bf \: {x}^{2} - {y}^{2} = (x + y)(x - y)}}}$

Hence,

$\boxed{ \red{\rm \: {x}^{3} - {2x}^{2} - x + 2 = (x - 2)(x - 1)(x + 1)}}$

Additional Information :-

↝ More Identities to know:

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a² - b² = (a + b)(a - b)

• (a + b)² = (a - b)² + 4ab

• (a - b)² = (a + b)² - 4ab

• (a + b)² + (a - b)² = 2(a² + b²)

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a - b)³ = a³ - b³ - 3ab(a - b)

Answer 2

Answer:

(x-1), (x+1), (x-2) it's the answer