1. 1.) Monomial - a number, variable, or product of either with only exponents of 0 or positive integers.
y, -x, ab, 1/3x, x2, 8, xy2, (abc2)3
Examples

2. Special Note
1.) Monomial - No monomial has a variable as an exponent, nor does it have a variable in the denominator of a fraction.
3/y, xa

3. Terms to write down
2.) Polynomial - is the sum or difference of monomials.
Any Monomial is also a polynomial
a-b, 7-x, -2x2 +xy-3,
1/8x - xy2, r + 9, 6
Examples

4. Adding Polynomials Add 5x + 7 and 8 - 2x (5x + 7) (-2x + 8) + =or

5. Adding Polynomials Add 5x + 7 and 8 - 2x line up the 5x + 7 -2x + 8
like terms +
3x + 15

6. Subtracting Polynomials
subtract 3a + b from 7a + 5b
(7a + 5b)
(3a + b) = -
7a + 5b -3a - b =
7a -3a + 5b - b
4a + 4b or

7. Subtracting Polynomials
Subtract 3a + b from 7a + 5b
line up the
(7a + 5b)
(3a + b)
like terms -
4a + 4b

8. c2 + 8c - 3 c2 + 5c + 4 3c - 7 c2 + 5c + 3c + 4 - 7 Adding Polynomials
Add c2 + 5c + 4 and 3c - 7
c2 + 5c + 4
3c - 7 + =
c2 + 5c + 3c
c2 + 8c - 3 or

9. c2 + 8c - 3 c2 + 5c + 4 3c - 7 Adding Polynomials
Add c2 + 5c + 4 and 3c - 7
line up the
c2 + 5c + 4
3c - 7
like terms +
c2 + 8c - 3

10. Monomials Have one term such as: 6, 7a, 5x2, -4m3n2 -4m3n2 Why is
a monomial?
-4m3n2

11. Binomials Have two terms such as 5x + 3, 6y2 - 2, a - b, 2x2y - 3xy2
Notice:
The terms are separated by one operation sign (+ or -)

12. Trinomials Have three terms such as: 3x2 + 5x - 6 -3m + m3 -2
Notice:
The terms are separated by two operation signs (+ or -)

13. Be ready to answer the following questions:
1.) What separates the terms of a polynomial?
2.) How many signs separate the terms of a trinomial?
operation signs 2

14. Which of these are monomials?
1.) x2 y2, x2 /y2, 1/7, ax2 + bx + c, 1/x + y
Why aren't the others
Monomials?

15. Which of these are Polynomials?
1.) x2 + y2, x3, x2 - 1/3, ax2 + bx + c, 1/x + y
Why isn't 1/x + y
a polynomial?

16. Clssifying Polynomial
Polynomials are Classified by degree.
The Degree is determined by the exponents of the terms.
For example:

17. The degree of a Monomial
Is the sum of the exponents of the variables of the monomial.
Monomial Degree x
x3 y2 5
3x3 y2 5
32x3 y2 5

18. The degree of a Monomial
Is the sum of the exponents of the variables of the monomial.
Monomial Degree x
x y

19. The degree of a Polynomial
Is the highest degree of any of its terms after the poly has been simplified.
Polynomial Degree
3x2 + 5x

20. The degree of a Polynomial
Polynomial Degree
3x2 + 5x
3x2 -9xyz +y+z
x + y
2x2 +7x -3y-2x

21. ascending
going up
the stairs

22. descending
going down
the stairs

23. Descending order of Polynomials
From the highest degree to the lowest degree of the terms.
3x2 + 5x + 7
3x3 + 5x2 - 2x + 7 2 1 2 1 3

24. Ascending order of Polynomials
From the lowest degree to the highest degree of the terms.
7 + 5x + 3x2
7 - 2x + 5x2 + 3x3 1 2 3 1 2