Given that \(4{{x}^{3}}-7{{x}^{2}}+6x-3=\left( 2{{x}^{2}}-4x+1 \right)\left( 2x+A \right)+Bx+C\

Question

Given that $4{{x}^{3}}-7{{x}^{2}}+6x-3=\left( 2{{x}^{2}}-4x+1 \right)\left( 2x+A \right)+Bx+C$ for all values of $x$, find the values of $A$, $B$, and $C$. Hence, find the remainder when the expression is divided by $\left( 2{{x}^{2}}-4x+1 \right)$.

Accepted Answer

$A = \frac{1}{2}, B = 6, C = -\frac{7}{2}$ ; ${6x - \frac{7}{2}}$

Polynomials, Cubic Equations and Partial Fractions - Polynomial Division and Remainders

Polynomials, Cubic Equations and Partial Fractions - Polynomial Division and Remainders

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