Using the factors (5x + 4)and (x - 1),find the remaining factor(s)of $f ( x ) = - 20 x ^ { 4 } + 109 x ^ { 3 } - 30 x ^ { 2 } - 79 x + 20$ and write the polynomial in fully factored form.
A) $f ( x ) = ( 5 x + 4 ) ( - x + 5 ) ( 4 x - 1 ) ( x - 1 )$
B) $f ( x ) = ( 5 x + 4 ) ^ { 2 } ( 4 x - 1 ) ( x + 1 )$
C) $f ( x ) = ( 5 x + 4 ) ( 5 x + 4 ) ( 4 x - 1 ) ( x - 1 )$
D) $f ( x ) = ( 5 x + 4 ) ^ { 2 } ( x - 1 ) ^ { 2 }$
E) $f ( x ) = ( 5 x + 4 ) ( - x - 5 ) ^ { 2 } ( x + 1 )$

Question

Using the factors (5x + 4)and (x - 1),find the remaining factor(s)of $f ( x ) = - 20 x ^ { 4 } + 109 x ^ { 3 } - 30 x ^ { 2 } - 79 x + 20$ and write the polynomial in fully factored form.
A)​ $f ( x ) = ( 5 x + 4 ) ( - x + 5 ) ( 4 x - 1 ) ( x - 1 )$
B)​ $f ( x ) = ( 5 x + 4 ) ^ { 2 } ( 4 x - 1 ) ( x + 1 )$
C)​ $f ( x ) = ( 5 x + 4 ) ( 5 x + 4 ) ( 4 x - 1 ) ( x - 1 )$
D)​ $f ( x ) = ( 5 x + 4 ) ^ { 2 } ( x - 1 ) ^ { 2 }$
E)​ $f ( x ) = ( 5 x + 4 ) ( - x - 5 ) ^ { 2 } ( x + 1 )$

Quizplus · Accepted Answer

Given the factors (5x + 4) and (x - 1), we can use polynomial division or synthetic division to find the remaining factors. The correct remaining factors, when multiplied with (5x + 4) and (x - 1), give the polynomial $f(x) = -20x^4 + 109x^3 - 30x^2 - 79x + 20$, which matches option A: $f(x) = (5x + 4)(-x + 5)(4x - 1)(x - 1)$. This option correctly represents the polynomial in its fully factored form.

Using the Factors (5x + 4)and (X - 1),find the Remaining