Determine the value of $k$ for which $x-2$ is a factor of \(\mathrm{f}\left( x \right)=4{{x}^{3}

Question

Determine the value of $k$ for which $x-2$ is a factor of $\mathrm{f}\left( x \right)=4{{x}^{3}}-5k{{x}^{2}}+2x-k$. Hence, find the remainder when $\mathrm{f}\left( x \right)$ is divided by $2x+3$.

Accepted Answer

$k = \frac{12}{7}$, Remainder $= -\frac{75}{2}$

Polynomials, Cubic Equations and Partial Fractions - Remainder and Factor Theorems

Polynomials, Cubic Equations and Partial Fractions - Remainder and Factor Theorems

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