Question

simplify this expression :-
x^3-2x-x+2

Answer 1

Step-by-step explanation:

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

Substitute x=1 in above polynomial then we will get 0 so x=1 is the root of this polynomial and (x-1) is a factor of this polynomial. Now divide this by (x-1)

(x-1)√x^3-3x+2 |(x^2+x-2)

-x^3+x^2

_____________

x^2-3x+2

-x^2+x

__________

-2x+2

2x-2

________

0

____

So we need to factorise

${x}^{2} + x - 2 = > {x}^{2} + 2x - x - 2 = >$

$x(x + 2) - 1(x + 2) = >$

$(x - 1)(x + 2) \: so \: {x}^{3} - 3x + 2 \:$

can be factorised as

${(x - 1)}^{2} (x + 2)$

Hope it helps you.

Answer 2

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