Solve the problem.
-Determine if the upper bound theorem identifies 4 as an upper bound for the real zeros of f (x). $$f ( x ) = 8 x ^ { 3 } - 8 x ^ { 2 } + 3 x - 9$$
A) Yes
B) No

Question

Quizplus · Accepted Answer

The upper bound theorem states that if you divide the polynomial by $x - c$ using synthetic division and all the numbers in the bottom row are positive or zero, then $c$ is an upper bound for the real zeros of the polynomial. In this case, if we use synthetic division with $c = 4$, we find that all the coefficients in the bottom row are positive or zero, indicating that 4 is indeed an upper bound for the real zeros of $f(x) = 8x^3 - 8x^2 + 3x - 9$.

Solve the Problem f(x)=8x3−8x2+3x−9f ( x ) = 8 x ^ { 3 } - 8 x ^ { 2 } + 3 x - 9f(x)=8x3−8x2+3x−9

Solve the Problem $f ( x ) = 8 x ^ { 3 } - 8 x ^ { 2 } + 3 x - 9$