(i)[2]
Determine the value of $a$.
(ii)[3]
With this value of $a$, factorise $p(x)$ fully.
(iii)[2]
Hence solve $p(e^y) = 0$, giving the answer correct to 2 significant figures.
Mathematics 9709 · AS & A Level · Logarithmic and exponential functions
Logarithmic and exponential functions — practice question
The polynomial $p(x)$ is given by $p(x) = ax^3 + ax^2 - 15x - 18$, with $a$ a constant. It is stated that $(x - 2)$ is a factor of $p(x)$.