Given that \(8{{x}^{3}}-32{{x}^{2}}+5x+12\equiv \left( Cx+D \right)\left( x-2 \right)\left( x+4

Question

Given that $8{{x}^{3}}-32{{x}^{2}}+5x+12\equiv \left( Cx+D \right)\left( x-2 \right)\left( x+4 \right)+A\left( x-2 \right)+B$ for all values of $x$, find the values of $A$, $B$, $C$ and $D$. Hence, or otherwise, deduce the remainder when $8{{x}^{3}}-32{{x}^{2}}+5x+12$ is divided by $x$ .

Accepted Answer

$A=165,\ B=-42,\ C=8,\ D=-48$. Remainder on division by $x$: $12$.

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

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

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