# Polynomial division with remainder problem [closed]

Not sure how to solve this one: If the remainder of dividing the polynomial $$x^{2018}-ax^{2017}+bx^{2015}+c$$ by $$x^3-x^2+x-1$$ is $$ax+b$$, where $$a,b,c\in\mathbb{R}$$, how much is $$a-b+c$$

## closed as off-topic by user296602, Xander Henderson, Leucippus, ccorn, choco_addictedOct 5 '18 at 6:15

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\begin{align*} x^{2018} - ax^{2017} + bx^{2015} + c = q(x)(x^{3} - x^{2} + x - 1) + ax + b \end{align*}
Secondly, notice that: \begin{align*} x^{3} - x^{2} + x - 1 = x^{2}(x-1) + (x - 1) = (x^{2} + 1)(x - 1) \end{align*}