Given that $6x^2 - 9x + 18 = A(2x + 1)(x - 1) + B(x - 2) + C$ for all values of $x$, find t

Question

Given that $6x^2 - 9x + 18 = A(2x + 1)(x - 1) + B(x - 2) + C$ for all values of $x$, find the values of $A$, $B$ and $C$.[3] Given that $ \mathrm{f}(x) = 2x^3 - 11x^2 + 3x + 36$, show that $2x + 3$ is a factor of $ \mathrm{f}(x)$ and hence solve the equation $ \mathrm{f}(x) = 0$.[5]

Accepted Answer

(a) $A=3$, $B=-6$, $C=9$ (b) $2x+3$ is a factor (shown), and $x=-\frac32,\ 3,\ 4$

2024 CCHY P1 Q6

2024 CCHY P1 Q6

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