When the expression $x^3+2kx+2$ is divided by $x+2$, the remainder is $3$ less than the remain

Question

When the expression $x^3+2kx+2$ is divided by $x+2$, the remainder is $3$ less than the remainder obtained when the expression is divided by $x-1$. Find the value of $k$.[3] Solve the equation $2x^3-5x^2-3x+10=0$, expressing non-integer roots in exact form.[4]

Accepted Answer

(a) $k=-1$ (b) $x=2$ or $x=\frac{1\pm\sqrt{41}}{4}$

2025 SCGS PRELIMS P2 Q5

2025 SCGS PRELIMS P2 Q5

Solution:

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