(i)[5]
Determine the values of $a$ and $b$.
(ii)[3]
Using these values of $a$ and $b$, factorise $p(x)$ fully.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
Let $p(x)$ denote the polynomial $8x^3 + ax^2 + bx - 1$, where $a$ and $b$ are constants. It is stated that $(x + 1)$ is a factor of $p(x)$ and that dividing $p(x)$ by $(2x + 1)$ leaves a remainder of $1$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Put $x=-1$, make the expression equal to zero, and simplify to $-8+a-b-1=0$” …
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