Given that $3{{x}^{3}}-8{{x}^{2}}+9x-7=\left( {{x}^{2}}-2x+3 \right)\left( 3x+A \right)+Bx+C$

Question

Given that $3{{x}^{3}}-8{{x}^{2}}+9x-7=\left( {{x}^{2}}-2x+3 \right)\left( 3x+A \right)+Bx+C$ for all values of $x$, find the values of $A$, $B$, and $C$. Hence, find the remainder when the expression is divided by $\left( {{x}^{2}}-2x+3 \right)$.

Accepted Answer

${A = -2, B = -4, C = -1}$; ${-4x - 1}$

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

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

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