Use the boundedness theorem to determine whether the statement is true or false.
-The polynomial $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$ has no real zero greater than 3 .

Question

Quizplus · Accepted Answer

The Boundedness Theorem states that if a polynomial is divided by $x - c$ and the remainder is positive, then there are no real zeros greater than $c$. Synthetic division of $f(x)$ by $x - 3$ yields a positive remainder, indicating no real zeros greater than 3.

Use the Boundedness Theorem to Determine Whether the Statement Is f(x)=x4−x3+2x2−4x−10f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10f(x)=x4−x3+2x2−4x−10

Use the Boundedness Theorem to Determine Whether the Statement Is $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$