The function $ \mathrm g\left( x \right)=2{{x}^{3}}+c{{x}^{2}}-9x+d$, where $c$ and $d$ a

Question

The function $ \mathrm g\left( x \right)=2{{x}^{3}}+c{{x}^{2}}-9x+d$, where $c$ and $d$ are constants, is exactly divisible by $x-2$ and leaves a remainder of $4$ when divided by $x+3$. Find the values of $c$ and $d$.

Accepted Answer

${c = \frac{29}{5}, d = -\frac{106}{5}}$

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

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

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