Given that $5{{x}^{3}}-17{{x}^{2}}+12x-6=({{x}^{2}}-3x+1)(5x+A)+Bx+C$ for all values of $x$

Question

Given that $5{{x}^{3}}-17{{x}^{2}}+12x-6=({{x}^{2}}-3x+1)(5x+A)+Bx+C$ for all values of $x$, find the value of $A$, of $B$ and of $C$. Hence, find the remainder when $5x^3-17x^2+12x-6$ is divided by $({{x}^{2}}-3x+1)$.

Accepted Answer

A=-2, B=1, C=-4; remainder=x-4.

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