Solve the polynomial equation by factoring and then using the zero product principle.
-$$4 x ^ { 4 } = 32 x$$
A) $\{ - 2,0,2 \}$
B) $\{ 0,4,2 \}$
C) $\{ 0 \}$
D) $\{ 0,2 \}$

Question

Quizplus · Accepted Answer

First, rewrite the equation as $4x^4 - 32x = 0$. Factor out the greatest common factor, $4x$, to get $4x(x^3 - 8) = 0$. Further factor $x^3 - 8$ as $(x - 2)(x^2 + 2x + 4)$. The solutions are $x = 0$ and $x = 2$, as $x^2 + 2x + 4$ has no real roots.

Solve the Polynomial Equation by Factoring and Then Using the Zero