Solve the radical equation, and check all proposed solutions.
-$$x ^ { 3 } + 5 x ^ { 2 } - x - 5 = 0$$
A) $\{ - 1,1 , - 5 \}$
B) $\{ 1 , - 5,5 \}$
C) $\{ - 5,5 \}$
D) $\{ 25 \}$

Question

Quizplus · Accepted Answer

This equation can be factored by grouping: $x^3 + 5x^2 - x - 5 = (x^2(x + 5) - 1(x + 5)) = (x^2 - 1)(x + 5) = (x + 1)(x - 1)(x + 5) = 0$, giving the solutions $x = -1, 1, -5$.

Solve the Radical Equation, and Check All Proposed Solutions x3+5x2−x−5=0x ^ { 3 } + 5 x ^ { 2 } - x - 5 = 0x3+5x2−x−5=0

Solve the Radical Equation, and Check All Proposed Solutions $x ^ { 3 } + 5 x ^ { 2 } - x - 5 = 0$