1. Find all the real zeros of the functions.
Students,
Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary.
Find all the real zeros of the functions.
Hint: Factor by grouping.

3. Remainder Theorem:
SYNTHETIC DIVISION
Only works when dividing by (x – k)
Try the first problem by using synthetic division.

4. Use the Remainder Theorem to evaluate.

5. Factor Theorem

7. Rational Root Theorem
If has integer coefficients, then every rational zero has the form:

8. Example) Find the rational zeros of
Step 1: List the possible zeros
Step 2: Test the possible zeros using Synthetic Division.

9. Use the Rational Root Theorem to find the zeros of the following functions.

11. Descartes’s Rule of Signs
1. Positive real zeros of f :
a) equal the number of sign variations of f(x) OR
b) less than number by an even integer
2. Negative real zeros of f:
a) equal the number of sign variations of f(–x) OR
b) less than number by an even integer

12. 3) Describe the possible real zeros of

13. Upper Bound
If c > 0 and each number in the last row is either positive or zero, c is an upper bound for the real zeros of f.
Lower Bound
If c < 0 and each number in the last row alternates positive and negative (zero counts as + & -), c is a lower bound for the real zeros of f.

14. 4) Given the upper and lower bounds of f, find the real zeros of f.

15. Sketch the graph of:

16. Write the following in standard form.
Solve the equation.