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It is known that $(3x + 1)$ is a factor of $p(x)$, and that dividing $p(x)$ by $(x - 2)$ leaves remainder $21$. Find the values of $a$ and $b$.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
The polynomial $ax^3 + bx^2 + x + 3$, with $a$ and $b$ as constants, is written as $p(x)$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $x=-\frac{1}{3}$ and form a correct equation, for example $-\frac{1}{27}a+\frac{1}{9}b-\frac{1}{3}+3=0$” …
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