Given that $2{{x}^{3}}+{{x}^{2}}-3x-4\equiv (2x+A)(x+1)(x-3)+B(x+1)+C$ for all values of $x$. Fi

Question

Given that $2{{x}^{3}}+{{x}^{2}}-3x-4\equiv (2x+A)(x+1)(x-3)+B(x+1)+C$ for all values of $x$. Find the values of $A$, $B$ and $C$. Hence, deduce the remainder when $2{{x}^{3}}+{{x}^{2}}-3x-4$ is divided by ${{x}^{2}}-2x-3$.

Accepted Answer

(a) A=5, B=13, C=-2; (b) remainder=13x+11.

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

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

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