1. Unit #4
Polynomials

2. The degree of a monomial is the sum of the exponents of the variables.
A monomial is the product of a constant times a variable raised to a nonnegative integer power.
The degree of a monomial is the sum of the exponents of the variables.
The coefficient is the real number of a term.

3. A polynomial is a monomial or the sum of monomials.
The degree of a polynomial is the monomial with the highest degree.

4. Variables with negative exponents
Polynomials cannot have the following:
Variables with negative exponents
Variable exponents
Variables under the radical sign

5. State the degree of the polynomial

6. Naming polynomials by the number of terms#
Name
Example 1
Monomial 4x 2
Binomial
2x + 3 3
Trinomial
4a² – 7a + 2 4
4th Term
4x – 2y + 9z – 6 5
5th Term
x³ – 4x²y + 7xy² + y³

7. Naming polynomials by the degree Names may only be used when the polynomial contains one variable
Example 1
Linear 4x 2
Quadratic
2a² + 9 3
Cubic
b³ – 4b + 6 4
Quartic 5
Quintic

8. Simplify the following expressions

9. Simplify the following expressions

10. Simplify the following expressions
Homework
Pages 33 – 34 #30 – 60 Even
Page 62 #61 – 68 All

11. Double Header in Baseball
Game
Probability Winning
Polynomial Form 1
1/3 2
5/8
What is the probability of 1 win and 1 loss ?
What is the probability of 2 wins ?
What is the probability of 2 losses ?

12. Three Game Series in Baseball
Probability Winning
Polynomial Form 1
2/3 2
1/5 3
2/7
What is the probability of 1 win and 2 losses ?
What is the probability of 2 wins and 1 loss ?
What is the probability of 3 wins ?

13. 2w + l, 1w + 4l, 2w + 5l

14. Two Game Series in Hockey
Prob Win
Prob Loss
Prob Tie
Poly Form 1
3/10
5/10
2/10 2
2/5
1/5
What is the probability of 1 win and 1 loss ?
What is the probability of 1 win and 1 tie ?

15. Binomial Theorem

17. Pascal’s Triangle 1 2 3 4 6 5 10 15 20 7 21 35

18. Binomial Theorem Notice each expression has n + 1 terms
The degree of each term is equal to n
The exponent of each a decreases by 1 and the exponent of each b increases by 1 for each succeeding term in the series
The coefficients come from Pascal’s Triangle
In subtraction alternate signs starting with positive then negative

19. Binomial Theorem
Write the general rule for the binomial using Pascal’s Triangle
Substitute into the general rule
Simplify your expression

20. Expand each of the following using the Binomial Theorem and Pascal’s Triangle

21. Factorial
If n > 0 is an integer, the factorial symbol n! is defined as follows:
n! = n(n – 1) •… • 3 • 2 • 1 if n > 2
0! = 1 and 1! = 1
4! = 4 • 3 • 2 • 1 = 24
6! = 6 • 5 • 4 • 3 • 2 • 1 = 720

22. Binomial Coefficient

23. Evaluate each of the following expressions

24. Expand each of the following using the Binomial Theorem and Factorials

25. We can use the Binomial Theorem to find a particular term in an expression without writing the entire expansion.

27. Monomial Division

28. Polynomial Division
List all of the terms with their powers in descending order
Replace any missing terms with a zero
Divide the polynomial until the degree of the divisor is greater than the degree of the remainder
Write the remainder over the divisor

29. Perform the indicated operation below