If x = $\frac { 3 } { 5 }$ is a root of $25 x ^ { 3 } - 105 x ^ { 2 } + 99 x - 27 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) $( 5 x - 3 ) ( 5 x + 3 ) ( x - 3 )$ x = $\frac { 3 } { 5 }$ , $- \frac { 3 } { 5 }$ , 3
B) $( 5 x + 3 ) ^ { 2 } ( x - 3 )$ x = $- \frac { 3 } { 5 }$ , 3
C) $( 5 x - 3 ) ( x - 3 ) ^ { 2 }$ x = $\frac { 3 } { 5 }$ , 3
D) $( 5 x + 3 ) ( x - 3 ) ^ { 2 }$ x = $- \frac { 3 } { 5 }$ , 3
E) $( 5 x - 3 ) ^ { 2 } ( x - 3 )$ x = $\frac { 3 } { 5 }$ , 3

Question

If x = $\frac { 3 } { 5 }$ is a root of $25 x ^ { 3 } - 105 x ^ { 2 } + 99 x - 27 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) $( 5 x - 3 ) ( 5 x + 3 ) ( x - 3 )$ x = $\frac { 3 } { 5 }$ , $- \frac { 3 } { 5 }$ , 3
B) $( 5 x + 3 ) ^ { 2 } ( x - 3 )$ x = $- \frac { 3 } { 5 }$ , 3
C)  $( 5 x - 3 ) ( x - 3 ) ^ { 2 }$ x = $\frac { 3 } { 5 }$ , 3
D) $( 5 x + 3 ) ( x - 3 ) ^ { 2 }$ x = $- \frac { 3 } { 5 }$ , 3
E) $( 5 x - 3 ) ^ { 2 } ( x - 3 )$ x = $\frac { 3 } { 5 }$ , 3

Quizplus · Accepted Answer

Given that $x = \frac{3}{5}$ is a root, we can use synthetic division to factor the polynomial. The correct factorization and roots are given by option E, which includes $(5x - 3)^2(x - 3)$, indicating that $x = \frac{3}{5}$ and $x = 3$ are the real solutions. The presence of the square term $(5x - 3)^2$ accounts for the given root $x = \frac{3}{5}$ being a repeated root, and $x - 3$ accounts for the root $x = 3$.

If X = 35\frac { 3 } { 5 }53​ Is a Root Of

If X = $\frac { 3 } { 5 }$ Is a Root Of