The polynomial $ P (x) = x^3 + ax^2 + bx + c$ is exactly divisible by $x^2 - 5x + 6$. Given that

Question

The polynomial $ P (x) = x^3 + ax^2 + bx + c$ is exactly divisible by $x^2 - 5x + 6$. Given that the remainder when $ P(x) $ is divided by $x + 1$ is $18$, find $a, b, c$

Accepted Answer

$a=-\dfrac52,\ b=-\dfrac{13}2,\ c=15$

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

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

Solution:

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