Question

question 9 of 10
the value 3 is an upper bound for the zeros of the function shown below.
$f(x) = -3x^3 + 20x^2 - 36x + 16$

a. true

b. false

Explanation:

Step1: Use synthetic division with 3

Coefficients: -3, 20, -36, 16.
Bring down -3. Multiply by 3: -9. Add to 20: 11.
Multiply 11 by 3: 33. Add to -36: -3.
Multiply -3 by 3: -9. Add to 16: 7.
Results: -3, 11, -3, 7 (alternating signs).

Step2: Apply upper bound rule

For positive k, if synthetic division results have no sign changes, k is upper bound. Here signs alternate, so 3 is not upper bound.

Answer:

B. False