Find values of b, c and d such that 1 and 4 are the only zeroes of \[ \begin{align} p(x) &= x^3 + bx^2 + cx + d \\ \end{align} \ \]
(a) Find a polynomial p(x) of degree 3 such that -1, 2 and 3 are zeroes and p(0) = 1.
(b) Suppose
\[ \begin{align}
p(x) &= 2x^5 + 5x^4 + 2x^3 - 1 \\
\end{align} \ \]
Explain why -1 is the only integer zero.