(i)[2]
Determine the value of $a$.
(ii)[3]
Using this value of $a$, factorise $p(x)$ in full.
(iii)[2]
Hence, solve the equation $p(e^y)=0$ and give the answer 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 $p(x)=ax^3+ax^2-15x-18$, where $a$ is a constant. It is stated that $(x-2)$ is a factor of $p(x)$.