# Worksheet: Upper and Lower Bound Tests for Polynomial Functions

Q1:

Hannah 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

Q2:

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

• 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 β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 .

• Aβ2, 2
• B1, 4
• Cβ4, 2
• D2, 13
• Eβ13, 1