The term containing the highest power of $x$ in the polynomial $\mathrm{f}(x)$ is $5{{x}^{3}}$

Question

The term containing the highest power of $x$ in the polynomial $\mathrm{f}(x)$ is $5{{x}^{3}}$. The roots of the equation $\mathrm{f}(x)=0$ are $-2$, $\mathrm{2}$ and $p$.

Find,

an expression, in terms of $x$ and $p$, for $\mathrm{f}(x)$ in descending powers of $x$,
the value of $p$ for which the division of $\mathrm{f}(x)$ by $x+1$ gives a remainder of $-30$,
the remainder when $\mathrm{f}(x)$ is divided by $2x+1$.

Accepted Answer

(a) $5x^3-5px^2-20x+20p$ (b) $p=-3$ (c) $-\frac{375}{8}$

Finding an Unknown Polynomial

Finding an Unknown Polynomial

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