1. Warm Up Create the following… a cubic binomial a quadratic trinomial
c) a 6th degree polynomial with 5 terms
d) a quintic monomial with two different variables
2) Simplify (4x3 + 2x – 1) – (-8 + 2x + 9x3 + x4)

2. HW Check – pg 1

3. Zeros and End Behavior

4. The “zero” of a function is just the value at which a function touches the x-axis.

5. Factored Polynomial (x - 3) and (x + 5) are factors of the polynomial.
It is easy to find the roots of a polynomial when it is in factored form!
(x - 3) and (x + 5) are factors of the polynomial.

6. (x - 3) and (x + 5) are factors of the polynomial.
(x - 3)(x + 5) = 0
(we want to know where the polynomial crosses the x-axis)
So (x – 3) = 0
and (x + 5) = 0
The zeros are x = 3, x = -5

7. Practice: Find the roots of the following factored polynomials.
y = (x-2)3(x+3)(x-4)
y = (x-5)(x+2)3(x-14)2
y = (x+3)(x-15)4
y = x2(x+6)(x-6)

8. Sometimes the polynomial won’t be factored!
Ex.

9. 2nd → TRACE (CALC) → 2: zero

10. Choose a point to the left of the zero. Then press ENTER.
This arrow indicates that you’ve chosen a point to the left of the zero.

11. Choose a point to the rightof the zero. Then press ENTER.
This arrow indicates that you’ve chosen a point to the right of the zero.

12. Press ENTER one more time!

13. Find the zeros of the following polynomials:

14. Solutions

15. End Behavior The end behavior of a graph
describes the far left and the far right portions of the graph.
We can determine the end behaviors of a polynomial using the leading coefficient and the degree of a polynomial.

16. First determine whether the degree of the polynomial is even or odd.
degree = 2 so it is even
Next determine whether the leading coefficient is positive or negative.
Leading coefficient = 2 so it is positive

17. Degree Even Odd Leading Coefficient + − High→High Low→High Low→Low

18. Find the end behavior of the following polynomials.