Find the remainder when the polynomial $5x^4-3x^3+2x-8$ is divided by $(x+1)$.

Step-by-step solution

1. Recognise that dividing by $(x+1)$ means using the root $x=-1$ (Remainder Theorem).
2. Substitute $x=-1$ into the polynomial: $5(-1{)}^4-3(-1{)}^3+2(-1)-8$.
3. Calculate each term: $5\times 1=5$, $-3\times (-1)=3$, $2\times (-1)=-2$, and $-8$ remains.
4. Add the terms: $5+3-2-8=-2$.
5. Thus the remainder is $-2$.

Concept tested: Remainder theorem

Published 24 August 2026 · How this solution was prepared and checked

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