Question

Factorize: x3-2x²-x+2.​

Answer 1

Answer:

3

−2x

2

−x+2

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

2

(x−2)−1(x−2)

= (x-2)( x^{2} -1)=(x−2)(x

2

−1)

= (x-2)(x+1)(x-1)=(x−2)(x+1)(x−1

Answer 2

Answer:

$\sf{The \ factorized \ form \ of \ x^{3}-2x^{2}-x+2} \\ \sf{is \ (x+1)(x-1)(x-2)}$

Solution:

$\sf{\leadsto{x^{3}-2x^{2}-x+2}} \\ \\ \sf{\leadsto{x^{2}(x-2)-1(x-2)}} \\ \\ \sf{\leadsto{(x^{2}-1)(x-2)}} \\ \\ \sf{Using \ identity \ a^{2}-b^{2}=(a+b)(a-b)} \\ \\ \sf{\leadsto{(x+1)(x-1)(x-2)}} \\ \\ \sf{Hence, \ the \ factorized \ form \ of \ x^{3}-2x^{2}-x+2} \\ \sf{is \ (x+1)(x-1)(x-2)}$

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Extra information:

• $\sf{(a-b)^{2}=(a+b)^{2}-4ab}$

• $\sf{(a+b)^{2}=(a-b)^{2}+4ab}$