Question

factorize x^3-2x^2-x+2​

Answer 1

Answer:

Factorise:-

$\bf\implies \: {x}^{3} - {2x}^{2} - x + 2$

$\bf\implies {x}^{3} - {x}^{2} - {x}^{2} + x - 2x + 2$

$\bf\implies {x}^{2} (x - 1) - x(x - 1) - 2(x - 1)$

$\bf\implies(x - 1)( {x}^{2} - x - 2)$

$\bf\implies(x - 1)( {x}^{2} + x - 2x - 2)$

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

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

@Indian Army

Answer 2

$\sf{\underline{\underline{\boxed{\huge{\red{\mathsf{ Solution }}}}}}}$

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

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

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

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

$\sf\longrightarrow ( x - 1 ) ( x^2 - 2x + x - 2 )$

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

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