Question

1 multiple choice 6 points solve the equation. $x^3 + 8x^2 - x - 8 = 0$ $\\{-1, 1, -8\\}$ $\\{-1, 1, 8\\}$ $\\{1, -2, 10\\}$ $\\{-1, 1, -9\\}$ clear my selection

Explanation:

Step1: Factor by grouping

Group the terms: $(x^3 + 8x^2) + (-x - 8) = 0$.
Factor out common terms: $x^2(x + 8) - 1(x + 8) = 0$.

Step2: Factor further

Factor out $(x + 8)$: $(x^2 - 1)(x + 8) = 0$.

Step3: Apply difference of squares

Factor $x^2 - 1$: $(x - 1)(x + 1)(x + 8) = 0$.

Step4: Solve for x

Set each factor to zero:
$x - 1 = 0 \implies x = 1$,
$x + 1 = 0 \implies x = -1$,
$x + 8 = 0 \implies x = -8$.

Answer:

$\{-1, 1, -8\}$