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This question already has an answer here:

How can we find the quotient and remainder when:

$$f(x)= x^5-x^4-4x^3+2x+3$$

is divided by $$g(x)=x-2?$$

Could someone please show how to step-by-step using synthetic division?

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marked as duplicate by jaykirby, Amzoti, Dan Rust, Start wearing purple, user67258 Aug 8 '13 at 13:33

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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A practical method is as follow:

$$\begin{align}\\ x^5-x^4-4x^3+2x+3&&&&& x-2\\ x^4-4x^3+2x+3 &&&&&x^4\\ -2x^3+2x+3 &&&&& x^3\\ -4x^2+2x+3 &&&&&-2x^2\\ -6x+3 &&&&&-4x\\ -9 &&&&&-6 \end{align}$$ so the quotient is $x^4+x^3-2x^2-4x-6$ and the remainder is $-9$.

and to explain the procedure of calculus: we divide the leading term $x^5$ of the dividend by the leading term $x$ of the divisor we find $x^4$ and then we calculate: $$x^5-x^4-4x^3+2x+3-x^4(x-2)=x^4-4x^3+2x+3=R(x)$$

and repeat the same calculus using $R(x)$ as your new dividend until we find the remainder $R(x)$ with degree less than the degree of the divisor $x-2$.

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I still want you to attempt the question since it is really a matter of applying the synthetic division. Where do you fail to understand it? See the example below where $f(x)=x^{5}-2x^{3}-3x^{2}$ and $g(x)=x-1$. Follow the steps

(1) If it is not clear, ask where it is unclear

(2) If it is clear, apply it to your question and we can confirm your answers

cheeers, abiyo enter image description here

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