Given that $x^2 - 1$ is a factor of $x^3 + ax^2 + bx - 2$, find the values of $a$ and $b$.

Question

Accepted Answer

$a = 2,\ b = -1$. Since $x^2 - 1 = (x-1)(x+1)$, both $f(1) = 0$ and $f(-1) = 0$. From $f(1)$: $1 + a + b - 2 = 0$, so $a + b = 1$. From $f(-1)$: $-1 + a - b - 2 = 0$, so $a - b = 3$. Adding gives $2a = 4$, $a = 2$, and then $b = -1$. Using only one of the two factors leaves a single equation and cannot fix both unkno

Answer

A) $a = 2,\ b = -1$

Answer

B) $a = -1,\ b = 2$

Answer

C) $a = 1,\ b = 0$

Answer

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

Given that $x^2 - 1$ is a factor of $x^3 + ax^2 + bx - 2$, find the values of $a$ and $b$.

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