1. Classifying Polynomials
7-6
Classifying Polynomials
What you WILL Learn:
1) To find the degree of a polynomial
2) To arrange the terms of a polynomial so that the powers of a variable are in ascending or descending order.

2. The prefix “mono” means 1
7-6
Monomial: one term (no + or -)
The prefix “mono” means 1
Can you name a monomial?

3. Binomial: two terms (separated by + or -) 7-6 The prefix “bi” means 2
Can you name a binomial?

4. Trinomial: three terms (separated by + or -)
7-6
Trinomial: three terms
(separated by + or -)
The prefix “tri” means 3
Can you name a trinomial?

5. The prefix “quad” means 4
7-6
Quadnomial: four terms
(separated by + or -)
The prefix “quad” means 4
Can you name a quadnomial?

6. The prefix “poly” means MANY
7-6
Polynomial: a monomial or a sum of monomials.
(separated by + or -)
The prefix “poly” means MANY
Can you name a polynomial?

7. 1/80z3 2. a8 – 1/5a + 2a 3. 2x + 6z 4. 4st3 + 1.2t2 – 0.8st Monomial
7-6
Determine the name of the polynomial.
1/80z a8 – 1/5a + 2a
3. 2x + 6z st t2 – 0.8st
Monomial
Trinomial
Binomial
Trinomial

8. 6) 5) Monomial Quadnomial 7) Polynomial 7-6
Determine the name of the polynomial. 6) 5)
Quadnomial
Monomial 7)
Polynomial

9. The degree of a MONOMIAL: the sum of the exponents of its variables.
7-6
The degree of a MONOMIAL: the sum of the exponents of its variables.
Example:
The degree of 5a2bc5 would be 8. 1
(2+1+5 = 8)

10. The degree of 2x2 + 9x3 + 4x5 would be 5.
7-6
The degree of a BINOMIAL, TRINOMIAL, QUADNOMIAL, or POLYNOMIAL: the GREATEST degree of all monomials in the polynomial.
Example:
The degree of 2x2 + 9x3 + 4x5 would be 5.

11. Next we are going to discuss the DEGREE.
7-6
Next we are going to discuss the DEGREE.
The degree helps us put things in order.
Think about where the degree symbol is for temperature… 71°… The degree symbol is in the exponent spot
When finding the degree, look at the exponent

12. Find the degree of the monomial or polynomial.
7-6
Find the degree of the monomial or polynomial. 7
5. d8 + h9 9 3
6. x8 + y9 – z10 +a4 10 11
7. a8 + 9a – 12a9 9 7

13. Find the degree of the monomial or polynomial.
7-6
Find the degree of the monomial or polynomial.
8. a8 + 9a2 + a6 8
9. 2x3 3
10. 7w5 + 2w +w4 5

14. The degree of a number is always zero!
7-6
The degree of a number is always zero!
The degree of 12 = 0
The degree of 3 = 0
The degree of -2 = 0

15. Linear means x Quadratic means x2 Cubic means x3 Quartic means x4
We also classify the polynomials based on the degree.
Linear means x
Quadratic means x2
Cubic means x3
Quartic means x4

16. ASCENDING: means increasing.
7-6
ASCENDING: means increasing.
If you are asked to put a polynomial in ascending order that means: Exponents go from SMALL TO BIG!
Example:
5 + 7x + 3x2

17. DESCENDING: means decreasing. Going from big to small.
7-6
DESCENDING: means decreasing. Going from big to small.
Descending Order: Exponents go from BIG TO SMALL!
*Numbers always go last because they have a degree of zero.
Example:
3x2 + 7x + 5

18. Descending order is often referred to as standard form.
You should always write your answers in standard form!

19. 2 + x4 + x2 6x – 3x2 + 4 – 2x8 x4 + x2 + 2 – 2x8 – 3x2 + 6x + 4
7-6
Rewrite the following in descending order.
2 + x4 + x2
6x – 3x2 + 4 – 2x8
x4 + x2 + 2
– 2x8 – 3x2 + 6x + 4
13. 7x6 + x – x3
7x6 – x3 + x2 +24

20. 2x4 + 3x Remember: A coefficient is a number in front of a variable.
7-6
Remember:
A coefficient is a number in front of a variable.
2x4 + 3x
Coefficient

21. 7-6
A leading coefficient is the coefficient of the FIRST TERM when the polynomial is written in descending order (standard form).
2x3 + 4x + 5
Leading coefficient

22. Leading coefficient = -1 -x5 + x4 + 2x +4;
7-6
Write the polynomial in descending order (standard form).
Then name the leading coefficient.
16.
Leading coefficient = 2
2x2 + 3x - 1;
17.
Leading coefficient = -1
-x5 + x4 + 2x +4;
18.
Leading coefficient = 4
4x3 + x2 + 2x – 7 ;