1. Polynomial Vocabulary and Adding & Subtracting Polynomials

2. Polynomial: expression involving many terms (poly=many nomial=terms)
Expression involving the sum of powers with one (or more) variables multiplied by coefficients.
The exponent must be a whole number (non-negative integer)
Ex. -9x3 + 4x2 – 7x + 8

3. Ex. the -9 , 4 , -7 are coefficients
Standard form: terms are written in descending order from the largest to the smallest degree (the exponent on the variable)
Ex. -9x3 + 4x2 – 7x + 8
12m5 + 9m
Coefficient: the number in front of the variable. (how many you have of each variable)
Ex. the -9 , 4 , -7 are coefficients
(8 is a constant not a coefficient)
the 12 and 9 are coefficients

4. Polynomials are named according to the number of terms they have
Term: each part of the polynomial (each product of a coefficient with a variable)
Ex. -9x3 + 4x2 – 7x + 8 has 4 terms,
the -9x3 , 4x2 , -7x , 8 are the 4 terms
Monomial: polynomial with one term
ex. 6x x k2
Binomial: polynomial with two terms
ex. 4x p5+8p g2 – 9g
Trinomial: polynomial with three terms
ex. 3x2-4x r8+2r6-r3

5. Polynomials are classified according to their degree
Degree: the degree of a polynomial is the largest degree (highest exponent) of any of its terms
Ex. -9x3 + 4x2 – 7x + 8 has a degree of 3
Linear: polynomial with degree of 1 (1st degree)
ex. 5x x - 4
Quadratic: polynomial with degree of 2 (2nd degree)
ex. -2p2+4p x2-5x-6
Cubic: polynomial with degree of 3 (3rd degree)
ex. 6x r3+5r2-r+3
Quartic: polynomial with degree of 4 (4th degree)
ex. x m4-m3+4m2-2m+1

6. Classifying Polynomials examples
Polynomial Degree
Classify Degree of Polynomial
Classify Polynomial Terms 6
Constant
Mononomial
-2x 1
Linear
3x+1
Binomial
-x2+2x-5 2
Quadratic
Trinomial
4x3-8x 3
Cubic
2x4-7x3-5x+1 4
Quartic

7. Name the degree and classify:
2x2 - x + 5
Degree: 2 Number of terms: 3
2nd degree quadratic trinomial
-5x3
Degree: 3 Number of terms: 1
3rd degree cubic monomial
-4x2 – 5 + 3x4 + 2x
3x4 – 4x2 + 2x - 5
put in standard form
Degree: Number of terms: 4
4th degree quartic polynomial

8. To Add and Subtract Polynomials
Combine like terms
You add or subtract the coefficients of each term with the same variable to the same power (do not change the actual variables or their powers)

9. Now Classify this by degree and terms:
Example: Add the polynomials
2x2 + x with x2 + x + 6
(2x2 + x - 5) + (x2 + x + 6)
= 2x2 + x2 + x + x
= 3x2 + 2x + 1
Remove ( )
distribute if needed
Combine like terms
Simplify
Now Classify this by degree and terms:
2nd Degree, Quadratic, Trinomial

10. Now Classify this by degree and terms:
Example: Subtract
-13x4 - 3x2 + 2x from 8x4 - 3x2 - 11x - 3
*Notice the order, means
(8x4-3x2-11x-3) – (-13x4-3x2+2x-17)
To Remove ( ) you must distribute the negative!
= 8x4 - 3x2 - 11x x4 + 3x2 - 2x + 17
= 21x4 - 13x + 14
Combine like terms
Simplify
Now Classify this by degree and terms:
4th Degree, Quartic, Trinomial

11. Subtract: (2x3 - 8) - (12x3 - 4x + 4) = 2x3 – 8 – 12x3 + 4x – 4
Practice Adding and Subtracting
Add: (-3x2 – 9) + (10x2)
= (-3x2 – 9) + (10x2)
= -3x2 – x2
= 7x2 - 9
2nd Degree, Quadratic, Binomial
Subtract: (2x3 - 8) - (12x3 - 4x + 4)
= 2x3 – 8 – 12x3 + 4x – 4
= -10x3+4x-12
3rd Degree, Cubic, Trinomial

12. Practice:
Match each expression with the equivalent polynomial D F A A E C