Solve the polynomial equation by factoring and then using the zero product principle.
-$$5 x ^ { 4 } = 135 x$$
A) $\{ 0,3 \}$
B) $\{ - 3,0,3 \}$
C) $\{ 0,5,3 \}$
D) $\{ 0 \}$

Question

Quizplus · Accepted Answer

First, factor out the common term, $x$, to get $5x^3 = 135$. Then, divide both sides by 5 to get $x^3 = 27$. Factoring further, we find $x^3 - 27 = 0$, which factors into $(x-3)(x^2+3x+9)=0$. The real roots are $x = 0$ (from the initial factoring of $x$) and $x = 3$ (from solving $x-3=0$).

Solve the Polynomial Equation by Factoring and Then Using the Zero