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

Question

Quizplus · Accepted Answer

To determine if $k = 2$ is a lower bound for the real zeros of the function $f(x) = 2x^3 + 3x^2 + 5x - 5$, the Descartes' Rule of Signs or the Rational Root Theorem could be used, but not synthetic division. Synthetic division is used to divide polynomials or to test possible rational zeros, not to directly determine upper or lower bounds of real zeros.

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

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