The expressions ${{x}^{3}}+a{{x}^{2}}-x+a$ and ${{x}^{3}}-{{x}^{2}}+a+2$ have the same remainder

Question

The expressions ${{x}^{3}}+a{{x}^{2}}-x+a$ and ${{x}^{3}}-{{x}^{2}}+a+2$ have the same remainder when divided by $(x-1)$, find the value of $a$, the remainder.

Accepted Answer

(i) a=2; (ii) remainder=4.

Polynomials, Cubic Equations and Partial Fractions - Remainder and Factor Theorems

Polynomials, Cubic Equations and Partial Fractions - Remainder and Factor Theorems

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