1. Intro to Polynomials

2. Polynomials
A monomial is the product of numbers, variables, or both. Ex. 5 x 6y 7jk2 A polynomial is a monomial or a group of monomials separated by + or –. Ex. 7x2 + 8xk - 4

3. What does each prefix mean?
mono bi tri

4. Naming a polynomial by Terms
Number of Terms
Name 1
Monomial 2
Binomial 3
Trinomial
4 or more
“with 4 terms”
(or 5 or 6, etc.)

5. State whether each expression is a polynomial. If it is, identify it.
1) 7y - 3x + 4
trinomial
2) 10x3yz2
monomial 3)
not a polynomial

6. The degree of a monomial is the sum of the exponents of the variables
The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial.
1) 5x2 2
4a4b3c 8 -3

7. To find the degree of a polynomial, use the monomial with the highest degree.
1) 8x2 - 2x + 7 Degrees: Which is biggest? 2 is the degree! 2) y7 + 6y4 + 3x4m4 Degrees: is the degree!

8. Find the degree of x5 – x3y2 + 42 3 5 10

9. Sometimes, a polynomial will already be factored
Sometimes, a polynomial will already be factored. When this is the case, add up all the exponents.
Ex. (x-2)3(x+5)2(x-3)(x+7)(x+1)3

10. Quick Recap
To find the degree of a polynomial, use the monomial with the largest degree. 7x3y + 9x2 + 4x + 5y If the polynomial is already factored, add up the exponents. (x-3)(x+4)(x-7) 3

11. Naming Polynomials by Degree
Name
Constant 1
Linear 2
Quadratic 3
Cubic 4
Quartic 5
Quintic 6+
(nth degree)
Naming Polynomials by Degree

12. Try it! Name the following polynomials:x3
x5 – xy + 3y2
t2 – 8
j4 + 6jk – 3j + 2

13. Adding and Subtracting Polynomials
Combine like terms.
Watch out for degrees! Don’t combine x and x2.
When subtracting, be sure to distribute the negative to all terms.

14. Example 1: Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a)

15. Example 2: Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2)

16. Example 3: Add the following polynomials: (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)

17. Example 4: Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a)

18. Example 5: Subtract the following polynomials: (7a - 10b) - (3a + 4b)

19. Example 6: Subtract the following polynomials: (4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2)

20. Find the sum or difference. (5a – 3b) + (2a + 6b)

21. Find the sum or difference. (5a – 3b) – (2a + 6b)