If $x = \frac { 2 } { 5 }$ is a root of $25 x ^ { 3 } - 70 x ^ { 2 } + 44 x - 8 = 0$, use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) $( 5 x - 2 ) ( 5 x + 2 ) ( x - 2 ) ; x = \frac { 2 } { 5 } , - \frac { 2 } { 5 } , 2$
B) $( 5 x + 2 ) ^ { 2 } ( x - 2 ) ; x = - \frac { 2 } { 5 } , 2$
C) $( 5 x - 2 ) ( x - 2 ) ^ { 2 } ; x = \frac { 2 } { 5 } , 2$
D) $( 5 x + 2 ) ( x - 2 ) ^ { 2 } ; x = - \frac { 2 } { 5 } , 2$
E) $( 5 x - 2 ) ^ { 2 } ( x - 2 ) ; x = \frac { 2 } { 5 } , 2$

Question

Quizplus · Accepted Answer

Given $x = \frac{2}{5}$ is a root, we can use synthetic division to factor the polynomial. The correct factorization and real solutions are found in option E, indicating that $(5x - 2)^2(x - 2)$ is the correct factorization, with real solutions $x = \frac{2}{5}$ and $x = 2$.

If x=25x = \frac { 2 } { 5 }x=52​ Is a Root Of

If $x = \frac { 2 } { 5 }$ Is a Root Of