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Find values for $a$ 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 $p(x)$. You are told that $(3x + 1)$ is a factor of $p(x)$, and that the remainder when $p(x)$ is divided by $(x - 2)$ is $21$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $x=-\frac{1}{3}$, set the result equal to zero or divide by $3x+1$ and set the remainder to zero, then form a correct equation, e.g. $-\frac{1}{27}a + \frac{1}{9}b - \frac{1}{3} + 3 = 0$” …
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