Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of
the function f.
-$k = 5 ; f ( x ) = 3 x ^ { 3 } - 3 x ^ { 2 } + 5 x - 2 ;$ Upper bound?
A) No
B) Yes

Question

Quizplus · Accepted Answer

The Descartes' Rule of Signs and the synthetic division process can be used to determine if a number is an upper bound for the real zeros of a polynomial. For $k = 5$, if we perform synthetic division and all the coefficients in the resulting polynomial are positive or zero, then $k$ is an upper bound. Given $f(x) = 3x^3 - 3x^2 + 5x - 2$, synthetic division with $k = 5$ will yield positive coefficients, indicating no sign changes and confirming that $k = 5$ is indeed an upper bound for the real zeros of $f(x)$.

Use Synthetic Division to Determine Whether the Number K Is k=5;f(x)=3x3−3x2+5x−2;k = 5 ; f ( x ) = 3 x ^ { 3 } - 3 x ^ { 2 } + 5 x - 2 ;k=5;f(x)=3x3−3x2+5x−2;

Use Synthetic Division to Determine Whether the Number K Is $k = 5 ; f ( x ) = 3 x ^ { 3 } - 3 x ^ { 2 } + 5 x - 2 ;$