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.
-$k = 2 ; f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 2 x + 5$; Lower bound?

Question

Quizplus · Accepted Answer

The Descartes' Rule of Signs or the use of synthetic division to test bounds for real zeros typically involves checking positive values of $k$ for upper bounds and negative values of $k$ for lower bounds. Since $k = 2$ is positive, it would be more appropriate to test if it is an upper bound, not a lower bound. Synthetic division itself doesn't directly determine if a number is an upper or lower bound but can be used in conjunction with the rule of signs or other methods to test specific values.

Use Synthetic Division to Determine Whether the Number K Is k=2;f(x)=x3−4x2−2x+5k = 2 ; f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 2 x + 5k=2;f(x)=x3−4x2−2x+5

Use Synthetic Division to Determine Whether the Number K Is $k = 2 ; f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 2 x + 5$