Which of the following linear factors is a factor of the polynomial $2x^3-3x^2-8x+12$?

Step-by-step solution

1. Use the factor theorem: a linear factor $(x-a)$ is a factor if $p(a)=0$.
2. Evaluate $p(2)=2(2{)}^3-3(2{)}^2-8(2)+12=16-12-16+12=0$.
3. Since $p(2)=0$, the factor $(x-2)$ divides the polynomial exactly.
4. The other options do not give zero when substituted, confirming $(x-2)$ as the correct factor.

Concept tested: Factor theorem

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

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