(i)[5]
Determine the values of $a$ and $b$.
(ii)[3]
When $a$ and $b$ take these values, determine the quotient and remainder when $p(x)$ is divided by $(x^2 - 2)$.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
Let $p(x)$ be the polynomial $2x^3 - 4x^2 + ax + b$, with $a$ and $b$ as constants. It is known that the remainder is $4$ when $p(x)$ is divided by $(x + 1)$, and that the remainder is $12$ when $p(x)$ is divided by $(x - 3)$.
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