If x = $\frac { 2 } { 7 }$ is a root of $49 x ^ { 3 } - 126 x ^ { 2 } + 60 x - 8 = 0$ ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) $( 7 x + 2 ) ^ { 2 } ( x - 2 )$ ;x = $- \frac { 2 } { 7 }$ ,2
B) $( 7 x - 2 ) ( x - 2 ) ^ { 2 }$ ;x = $\frac { 2 } { 7 }$ ,2
C) $( 7 x + 2 ) ( x - 2 ) ^ { 2 }$ ;x = $- \frac { 2 } { 7 }$ ,2
D) $( 7 x - 2 ) ^ { 2 } ( x - 2 )$ ;x = $\frac { 2 } { 7 }$ ,2
E) $( 7 x - 2 ) ( 7 x + 2 ) ( x - 2 )$ ;x = $\frac { 2 } { 7 }$ , $- \frac { 2 } { 7 }$ ,2

Question

If x = $\frac { 2 } { 7 }$ is a root of $49 x ^ { 3 } - 126 x ^ { 2 } + 60 x - 8 = 0$ ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A)​ $( 7 x + 2 ) ^ { 2 } ( x - 2 )$ ;x = $- \frac { 2 } { 7 }$ ,2
B) $( 7 x - 2 ) ( x - 2 ) ^ { 2 }$ ;x = $\frac { 2 } { 7 }$ ,2
C) $( 7 x + 2 ) ( x - 2 ) ^ { 2 }$ ;x = $- \frac { 2 } { 7 }$ ,2
D) $( 7 x - 2 ) ^ { 2 } ( x - 2 )$ ;x = $\frac { 2 } { 7 }$ ,2
E) $( 7 x - 2 ) ( 7 x + 2 ) ( x - 2 )$ ;x = $\frac { 2 } { 7 }$ , $- \frac { 2 } { 7 }$ ,2

Quizplus · Accepted Answer

Using synthetic division with $x = \frac{2}{7}$, we can factor the polynomial and find that the correct factorization is $(7x - 2)^2(x - 2)$, which gives the real solutions $x = \frac{2}{7}$ and $x = 2$.

If X = 27\frac { 2 } { 7 }72​ Is a Root Of

If X = $\frac { 2 } { 7 }$ Is a Root Of