When a polynomial $\mathrm{f}\left( x \right)$ is divided by $x-2$ and $x-4$, the remainder is

Question

When a polynomial $\mathrm{f}\left( x \right)$ is divided by $x-2$ and $x-4$, the remainder is $-1$ and $7$ respectively. Find the remainder when $\mathrm{f}\left( x \right)$ is divided by $\left( x-2 \right)\left( x-4 \right)$. Given that the polynomial ${{x}^{2}}-2x+6$ leaves the same remainder when it is divided by $x-p$ and $x+3q$, find the value of $p-3q$ when $p\ne -3q$.

Accepted Answer

(a) $R(x)=4x-9$ (b) $p-3q=2$

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

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

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