The polynomial $g(x) = mx^3 - 8x^2 - 9x + n$ has a factor of $3x - 2$ and leaves a remainder of

Question

The polynomial $g(x) = mx^3 - 8x^2 - 9x + n$ has a factor of $3x - 2$ and leaves a remainder of $6$ when divided by $x$. Find the values of $m$ and $n$.[3] Using the values of $m$ and $n$ from (a), solve, in exact form, the equation $g(x) = 0$.[3] Hence solve the equation $9e^{2y} + 8e^y = 12 + 6e^{3y}$.[3]

Accepted Answer

(a) $m=12$, $n=6$ (b) $x=\dfrac23$ or $x=\pm\dfrac{\sqrt3}{2}$ (c) $y=\ln\left(\dfrac32\right)$ or $\ln\left(\dfrac2{\sqrt3}\right)$

2023 Ahmad Ibrahim Sec AM S3 EOY Q9

2023 Ahmad Ibrahim Sec AM S3 EOY Q9

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