QuestionProve that $2 x^{4}-6 x^{3}+3 x^{2}+3 x-2$ is divisible by $x^{2}-3 x+2$ without division.

Studdy Solution
Since the given polynomial is divisible by both $(x-)$ and $(x-)$, it is divisible by their product, which is the divisor $x^{}-3 x+$.
Therefore, without actual division, we have proved that $x^{4}-6 x^{3}+3 x^{}+3 x-$ is exactly divisible by $x^{}-3 x+$.