# Worksheet: Remainder and Factor Theorem with Synthetic Division

In this worksheet, we will practice identifying factors and zeros and finding the remainder of a polynomial function using the remainder and factor theorem with synthetic division.

**Q3: **

Consider the function .

Given that two of the three numbers , and 3 are roots of , use synthetic division to fully factor .

- A
- B
- C
- D
- E

**Q5: **

The function has 2 real zeros and 2 imaginary zeros.

Using synthetic substitution, determine which of the values 1, 2, 3, and 4 is a root of and write in the form .

- A
- B
- C
- D
- E

Using synthetic substitution, determine which of the values , , , and is a root of and write in the form .

- A
- B
- C
- D
- E

State all the zeros of .

- A, 1, ,
- B2, , ,
- C4, , ,
- D4, 1, ,
- E2, , ,