In this worksheet, we will practice using upper and lower bound tests to verify if the given interval is the interval that contains all real zeros.

**Q1: **

Using synthetic division and the upper and lower bound tests, find all real zeros of the function .

- A
- B
- C
- D
- E

**Q2: **

Rania is trying to find zeros in the function . She has used synthetic division to find for , , 1, and 3.

Use her results to state an interval in which all real zeros of lie.

- A
- B
- C
- D
- E

**Q3: **

Consider the function .

William is using synthetic division to help him find real zeros of .

What can he conclude about −5?

- AThat it is a real zero of
- BThat it is an upper bound on the interval in which all real zeros lie
- CThat it is neither upper bound nor lower bound on the interval in which all real zeros lie
- DThat it is a lower bound on the interval in which all real zeros lie

What can he conclude about 2?

- AThat it is a real zero of
- BThat it is the only real zero of
- CThat it is a lower bound on the interval in which all real zeros lie

Find all the real zeros of .

- A−2, 2
- B1, 4
- C−4, 2
- D2, 13
- E−13, 1