1. 4-1 Polynomial Functions

2. Notes Monomial – one term: 3x Binomial – two terms: 2x + 7
Trinomial – three terms: 3x2 – 4x + 7
Polynomial – many terms: 5x3 – 2x2 + 4x + 8
Degree – largest sum of exponents on a monomial

3. Examples Tell if a monomial, binomial or trinomial. 7y4 – 4y2 + 2
10x3y2

4. Examples Find the degree of the polynomial. 3) 3x2 + 5
4) y7 + y5 - 3x4y4
5) p5 + p3m3 + 4m

5. Zeros of a function: Where f(x) = 0
Imaginary number (i) = √-1
i0- i=
i2=
i3=
I4=

6. Fundamental theorem of Algebra: for each polynomial with degree n, there are n solutions. (some may be real, some imaginary)
Example: x2 has 2 solutions, x3 has three solutions

7. General Shapes of Polynomials

8. 1) Write a polynomial with roots 4 and 2 2) Write a polynomial with roots 2, 4i, -4i.

9. State the number of roots in the equation
9x4 -35x2 -4=0. Find them.

10. Multiplying Polynomials
“FOIL” 3) (3x + 3) (2x – 4) 4) (2x -1 ) (x2 + 3x + 1)

11. Binomial Expansion
Remember Pascal's triangle?

12. (x + y)6 (3x + 2y)4

14. Dividing
Long Division x2 + 3x -8 ÷ x -2

15. Synthetic Division
Make sure there is no leading coefficient. It should be in the form “ x-r”
2) Arrange the coefficients in a line. (If you are missing a term, use 0)
3) Place the number r in front of the box. Use opposite sign
4) Bring down first number
5) Multiply/Add/Multiply/Add

16. x3 +4x2 -3x-5 ÷ x+3

17. (x3 –x2+2) ÷ (x + 1)