Question

divide x cube minus 3 x square minus x + 3 by X + 1 and verify the division algorithm

Answer 1

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Answer 2

Answer:

Division algorithm is proved.

Step-by-step explanation:

According to the question , we are given a equation $x^{3}-3x^{2} -x+3$ . We need to divide the equation by $x+1$.

$\frac{x^{3}-3x^{2} -x+3}{x+1}\\ \\=\frac{x^{3}+x^{2} -4x^{2} -4x+3x+3}{x+1}\\ \\= \frac{x^{2}(x+1)-4x(x+1)+3(x+1) }{x+1}\\ \\= \frac{(x+1)(x^{2} -4x+3)}{x+1}\\ \\= x^{2} -4x+3$

According to the division algorithm ,

Divident = divisor * quotient + remainder

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

Divisor * quotient + remainder = $(x+1)$$(x^{2} -4x+3)$$+0$ = $x^{3}-3x^{2} -x+3$

So , division algorithm is proved.

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