Solve the polynomial equation by factoring and then using the zero product principle.
-$$x ^ { 3 } + 8 x ^ { 2 } - x - 8 = 0$$
A) $\{ - 8,8 \}$
B) $\{ - 1,1 , - 8 \}$
C) $\{ 64 \}$
D) $\{ 1 , - 8,8 \}$

Question

Quizplus · Accepted Answer

The polynomial can be factored by grouping: $x^3 + 8x^2 - x - 8 = (x^2(x + 8)) - (1(x + 8)) = (x^2 - 1)(x + 8) = (x + 1)(x - 1)(x + 8)$. Setting each factor equal to zero gives the solutions $x = -1, 1, -8$.

Solve the Polynomial Equation by Factoring and Then Using the Zero