The function $\mathrm{f}(x)=3{{x}^{3}}+a{{x}^{2}}-10x+b$, where $a$ and $b$ are constants

Question

The function $\mathrm{f}(x)=3{{x}^{3}}+a{{x}^{2}}-10x+b$, where $a$ and $b$ are constants, is exactly divisible by $x-4$ and leaves a remainder of $5$ when divided by $x+1$. Find the value of $a$ and of $b$.

Accepted Answer

$a=-10,\ b=8$

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

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

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