If x = -4 is a root of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) $( x + 5 ) ( x - 5 ) ( x - 4 ) ; x = - 5,5,4$
B) $( x + 5 ) ^ { 2 } ( x + 4 ) ; x = - 5 , - 4$
C) $( x + 5 ) ( x + 4 ) ^ { 2 } ; x = - 5 , - 4$
D) $( x - 5 ) ( x + 4 ) ( x - 4 ) ; x = 5 , - 4,4$
E) $( x + 5 ) ( x + 4 ) ( x - 4 ) ; x = - 5 , - 4,4$

Question

Quizplus · Accepted Answer

Using synthetic division with $x = -4$, the polynomial $x^3 + 5x^2 - 16x - 80$ can be factored to $(x + 4)(x^2 + x - 20)$. Further factoring $x^2 + x - 20$ gives $(x + 5)(x - 4)$, resulting in the complete factorization $(x + 5)(x + 4)(x - 4)$ and the real solutions $x = -5, -4, 4$.

If X = -4 Is a Root Of x3+5x2−16x−80=0x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0x3+5x2−16x−80=0

If X = -4 Is a Root Of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$