Find the quotient and the remainder when x^{3 | vedclass

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(A) To find the quotient and remainder,we perform polynomial long division of $(x^{3}+x^{2}-10x+8)$ by $(x-1)$.Step $1$: Divide the first term of the

Vedclass · Accepted Answer

Quotient $= x^{2}+2x-8$,Remainder $= 0$

Vedclass · Answer

(A) To find the quotient and remainder,we perform polynomial long division of $(x^{3}+x^{2}-10x+8)$ by $(x-1)$.Step $1$: Divide the first term of the dividend $x^3$ by the first term of the divisor $x$ to get $x^2$.Step $2$: Multiply $x^2$ by $(x-1)$ to get $(x^3-x^2)$. Subtract this from the dividend: $(x^3+x^2-10x+8) - (x^3-x^2) = 2x^2-10x+8$.Step $3$: Divide the first term of the new polynomial $2x^2$ by $x$ to get $2x$.Step $4$: Multiply $2x$ by $(x-1)$ to get $(2x^2-2x)$. Subtract this: $(2x^2-10x+8) - (2x^2-2x) = -8x+8$.Step $5$: Divide the first term $-8x$ by $x$ to get $-8$.Step $6$: Multiply $-8$ by $(x-1)$ to get $(-8x+8)$. Subtract this: $(-8x+8) - (-8x+8) = 0$.Thus,the Quotient is $x^{2}+2x-8$ and the Remainder is $0$.

Find the quotient and the remainder when $x^{3}+x^{2}-10x+8$ is divided by $x-1$.

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