(i)[2]
If $(x + 2)$ is a factor of $p(x)$, determine the value of $a$.
(ii)[5]
With this value of $a$, determine the quotient when $p(x)$ is divided by $(x + 2)$ and then show that $p(x) = 0$ has exactly one real root.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
The polynomial $p(x)$ is given by $p(x) = x^3 + 2x + a$, where $a$ is a constant.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set $x=-2$ and make the expression equal to zero, or perform division and set the remainder equal to zero” …
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