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

Question

The polynomial ${\mathrm{g}(x) = mx^3 - 8x^2 - 9x + n}$ 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 ${\mathrm{g}(x) = 0}$.[3] Hence solve the equation ${9e^{2y} + 8e^y = 12 + 6e^{3y}}$.[3]

Accepted Answer

(a) $n = 6$, $m = 12$ (b) $x = \frac{2}{3}$ \text{ or } $x = \pm\frac{\sqrt{3}}{2}$ (c) $y = 0.405$ \text{ or } $y = 0.144$

2023 AISS AM S3 EOY Q9

2023 AISS AM S3 EOY Q9

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