Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational
roots.
-$$x ^ { 3 } - 8 x ^ { 2 } - x + 8 = 0$$
A) $\{ 1 , - 1,8 \}$
B) $\{ - 1,2 , - 4 \}$
C) $\{ 1,2,4 \}$
D) $\{ 1 , - 1 , - 8 \}$

Question

Quizplus · Accepted Answer

The possible rational roots are $\pm 1, \pm 2, \pm 4, \pm 8$. Using synthetic division, we find that $x = 1$ is a root. Dividing $x^3 - 8x^2 - x + 8$ by $x - 1$, we get $x^2 - 7x - 8$. Factoring this quadratic, we get $(x - 8)(x + 1)$. Therefore, the roots are $x = 1, x = 8, x = -1$.

Solve the Polynomial Equation x3−8x2−x+8=0x ^ { 3 } - 8 x ^ { 2 } - x + 8 = 0x3−8x2−x+8=0

Solve the Polynomial Equation $x ^ { 3 } - 8 x ^ { 2 } - x + 8 = 0$