When the polynomial $f(x) = x^3 - 2x^2 + ax + b$ is divided by $(x - 1)$, the remainder is 4, and when divided by $(x + 1)$, the remainder is -2. Find the values of $a$ and $b$.

Question

Accepted Answer

$a = 2, b = 3$. f(1) = 1 - 2 + a + b = 4 gives a + b = 5. f(-1) = -1 - 2 - a + b = -2 gives -a + b = 1. Solving simultaneously: adding gives 2b = 6, so b = 3... wait, let me recheck: a+b=5 and -a+b=1, adding: 2b=6, b=3, a=2. The correct answer is B. [Correction: answer should be B]

Answer

A) $a = 3, b = 2$

Answer

B) $a = 2, b = 3$

Answer

C) $a = -3, b = 2$

Answer

D) $a = 3, b = -2$

When the polynomial $f(x) = x^3 - 2x^2 + ax + b$ is divided by $(x - 1)$, the remainder is 4, and when divided by $(x + 1)$, the remainder is -2. Find the values of $a$ and $b$.

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