1. EQ – what is a polynomial, and how can I tell if a term is one?
Polynomials
Polynomials
EQ – what is a polynomial, and how can I tell if a term is one?

2. Terms:
Monomial – a number or product of numbers and variables with exponents that are whole numbers
Examples: 2n, x3, 4a5b6, 7
Non Examples: p2.4, 2x, ,

3. Polynomial – one monomial or the sum or difference of monomials
Examples: , , , x+4
Non-Examples: , ,

4. Polynomials are classified by their number of terms
One term – monomial
Two terms – binomial
Three terms – trinomial
Four or more-polynomial

5. Polynomials are also classified by degrees.
The degree of a polynomial is the same as the term with the greatest degree
Degree Degree Degree Degree 0
This polynomial has a degree of 5

6. Degrees of a Polynomial
Leading coefficient is in front of the highest degree term.
A constant can be a leading coefficient if by itself.
O - constant
1st – linear
2nd-Quadratic
3rd-Cubic
4th-Quartic
Standard form –polynomial in descending order of degrees.

7. Simplifying Polynomials
You can simplify a polynomial by adding or subtracting like terms ( they must have the same variable and the same degree)
Or you can simplify one using the distributive property
Leading coefficient - coefficient in front of the term with highest degree.

8. Combining like terms

10. Try these:

11. Using the Distributive Property

12. Try these:

13. Adding Polynomials
To add two polynomials, you can combine like terms or line up the like terms and add them vertically.
Horizontal format
Vertical format

15. To add them vertically:

16. Try these:

17. Subtracting Polynomials
This is like adding the opposite -- find the opposite of the second number and then add like you did before
Horizontal format
Vertical format

18. Finding the opposite

19. To Subtract:

20. Try these:

21. Multiplying polynomials by monomials

22. Or you may need the distributive property

23. Try these:

24. Multiplying binomials
Think FOIL
(first, outside, inside, and last)
This is the order you will multiply them!

25. Check out these examples:

26. Try these:

27. Factoring Polynomials
Factoring is dividing out factors that are the same in the polynomial
Factoring binomials are reversing FOIL.

28. Factoring
Taking out the GCF of the terms of a polynomial.

29. Leading coefficient not 1

30. Special factoring
Patterns in factoring…

31. Try these:

32. The End