Given that $12{{x}^{3}}-61{{x}^{2}}+4x+16\equiv (Ax+B)(x-1)(x+3)+C(x-1)+D$ for all values of $x$

Question

Given that $12{{x}^{3}}-61{{x}^{2}}+4x+16\equiv (Ax+B)(x-1)(x+3)+C(x-1)+D$ for all values of $x$, find the values of $A$, $B$, $C$ and $D$. Hence, or otherwise, deduce the remainder when $12{{x}^{3}}-61{{x}^{2}}+4x+16$ is divided by${{x}^{2}}+2x-3$.

Accepted Answer

$A=12,\ B=-85,\ C=210,\ D=-29$ Remainder $=210x-239$

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

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

Video Solution:

Solution:

Solution locked