Question

Mark (✓) against the correct answer in each of the following:
If p(x) = x³ + x² + ax + 115 is exactly divisible by (x + 5) then a = ?
(a) 8
(b) 6
(c) 5
(d) 3

Answer 1

(d) 3

p(x) = x³ + x² + ax + 115 is exactly divisible by (x + 5).
Therefore, p($-$5) = 0$$
$$\begin{gathered} \Rightarrow {\left(-5\right)}^3+{\left(-5\right)}^2+a\times \left(-5\right)+115=0 \\ \Rightarrow -125+25-5a+115=0 \\ \Rightarrow -5a+15=0 \\ \Rightarrow 5a=15 \\ \therefore a=3 \end{gathered}$$