Find a rational zero of the polynomial function and use it to find all the zeros of the function.
-$$f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$$
A) $\{ 1 , - 1,8 \}$
B) $\{ - 1,2 , - 4 \}$
C) $\{ 1,2,4 \}$
D) $\{ 1 , - 1 , - 8 \}$

Question

Quizplus · Accepted Answer

By the Rational Zero Theorem, the possible rational zeros are $\pm 1, \pm 2, \pm 4, \pm 8$. Testing these values, we find that $x = 1$ is a zero. Using synthetic division, we can find the other zeros:```1 | 1 -8 -1  8   | 1 -7 -8   ----------------   | 1 -7 -9  0```So, the other zeros are $x = -7$ and $x = 0$. Therefore, the zeros of the function are $x = 1, -7, 0$.

Find a Rational Zero of the Polynomial Function and Use f(x)=x3−8x2−x+8f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8f(x)=x3−8x2−x+8

Find a Rational Zero of the Polynomial Function and Use $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$