1. Unit #2
Polynomials

2. What are we going to do… Find the degree of a polynomial.
Arrange the terms of a polynomial is ascending or descending order.

3. Polynomial
A polynomial is a monomial or a sum or difference of monomials.
Examples 2x
x2 – 16
x2 – x – 56

4. Binomial A binomial is the sum or difference of two monomials.
Examples
x + 1
3x2 – 4x
5xy2 + 3x2yz

5. Trinomial A trinomial is the sum or difference of three monomials.
Examples
x2 + 2x + 10
4ab2 – ab + 7
-7cd3 – 4cd2 + cd

6. POLYNOMIALS
Trinomials
Binomials

7. Degree of a Monomial
The degree of a monomial is the sum of the exponents of all its variables.
8y4 degree 4
3a degree 1
-2xy2z3 degree 6
7 degree 0

8. Degree of a Polynomial
The degree of a polynomial is the greatest degree of any monomial contained in the polynomial.
5mn2 degree 3
-4x2y2 + 3x degree 4
3a + 7ab – 2a2b + 16 degree 3

9. Ascending Order
To write a polynomial in ascending order, start with the lowest power and work your way to the highest power.
x3 + 2x – x2
16 + 2x – x2 + 14x3
REMEMBER:
(LOWEST  HIGHEST)
The sign in front of the numbers, stays with the number!

10. Descending Order
To write a polynomial in descending order, start with the highest power and work your way down to the lowest power.
a4 + ax2 – 2a3xy3 – 9x4y
-9x4y + ax2 – 2a3xy3 + a4
REMEMBER:
(HIGHEST  LOWEST)
The sign in front of the number, stays with the number!

11. Find the degree: Example 1:

12. Example 2:
2x3 – 4y + 7xy
degree 3

13. Example 3:
7 + d5 – b2c2d3 + b6
degree 7

14. Example 1: Arrange the polynomial in ascending order:
2x + 3x2 – 1
-1 + 2x + 3x2

15. Example 2: Arrange the polynomial in ascending order:
-5x2 + 3x + 4x5 - 2
-2 + 3x - 5x2 + 4x5

16. Example 3: Arrange the polynomial in ascending order:
-4x2y + 3xy – 5x3y2
3xy – 4x2y – 5x3y2

17. Example 4: Arrange the polynomial in descending order:
5 + x5 + 3x3
x5 + 3x3 + 5

18. Example 5: Arrange the polynomial in descending order:
-1 + 3x2 + 2x
3x2 + 2x - 1

19. Example 6: Arrange the polynomial in descending order:
-3x2y2 + 2xy – 3x3y
-3x3y – 3x2y2 + 2xy