Answer:
The answer is **B. False**. The number 4 is not an upper bound for the set of roots of this polynomial function.
To see why, we can use the **rational root theorem**, which states that if a polynomial function has rational roots, then they must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is 2 and the leading coefficient is 3, so the possible rational roots are:
±1, ±2, ±1/3, ±2/3
We can use **synthetic division** to test each of these possible roots and see if they give a remainder of zero, which means they are actual roots.
If we try 4, we get:
| 4 | 3 | -5 | -5 | 5 | 2 |
|---|---|----|----|---|---|
| | | 12 | 28 | 92 | 388 |
|---|---|----|----|---|---|
| | 3 | 7 | 23 | 97 | 390 |
The remainder is 390, which is not zero, so 4 is not a root of the polynomial function.
Therefore, 4 is not an upper bound for the set of roots of this polynomial function.
: [Rational Root Theorem]
: [Synthetic Division]
Explanation: