Solve the polynomial equation by factoring and then using the zero product principle.
-$$3 x - 5 = 48 x ^ { 3 } - 80 x ^ { 2 }$$
A) $\left\{ 0 , \frac { 5 } { 3 } \right\}$
B) $\left\{ - \frac { 1 } { 4 } , \frac { 1 } { 4 } , \frac { 3 } { 5 } \right\}$
C) $\left\{ - \frac { 1 } { 4 } , \frac { 1 } { 4 } , \frac { 5 } { 3 } \right\}$
D) $\left\{ - \frac { 1 } { 16 } , \frac { 1 } { 16 } , \frac { 5 } { 3 } \right\}$

Question

Quizplus · Accepted Answer

Rearrange the equation to $48x^3 - 80x^2 - 3x + 5 = 0$. Factor by grouping: $x(48x^2 - 80x - 3) + 5 = 0$. Solve for roots: $x = 0$, $x = \frac{5}{3}$, and factor the quadratic to find $x = \pm \frac{1}{4}$.

Solve the Polynomial Equation by Factoring and Then Using the Zero