Mathematics 9709 · AS & A Level · Logarithmic and exponential functions

Logarithmic and exponential functions — practice question

The polynomial $p(x)$ is given by $p(x) = 4x^3 + 4x^2 - 29x - 15$.
(i)[2]

Show, using the factor theorem, that $(x + 3)$ is a factor of $p(x)$.

(ii)[3]

Fully factorise $p(x)$.

(iii)[3]

Hence, for the equation $2^{3u+2} + 4^{u+1} = 29 \times 2^u + 15$, determine the value of $2^u$ and, by using logarithms, determine $u$ correct to 3 significant figures.

(c(iii))[3]

Hence, for the equation $2^{3u+2} + 4^{u+1} = 29 \times 2^u + 15$, work out the value of $2^u$ and, by using logarithms, work out $u$ correct to 3 significant figures.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Put $x=-3$ into the expression and simplify

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