1. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Chapter 6: Polynomials
Section 6.2: Polynomials: Classification, Addition, and Subtraction

2. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Goal: To classify, add, and subtract polynomials

3. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Monomial – polynomial with one term
Ex: 2x xyz ½ a
Binomial – polynomial with 2 terms
2x x – x2 + 4
Trinomial - polynomial with 3 terms
7x2 + 8x – ½ x + 3y – 2z

4. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Degree – To determine the degree of a monomial, add the exponents for each variable
Degree of a polynomial – the degree of the monomial with the greatest degree.
3430r r has a degree of 2
Leading coefficient - coefficient of the first term
Standard form

5. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Example 1
Determine whether each expression is a polynomial. If it is a polynomial, state the degree of a the polynomial.
c4 – 4√c + 18
-16p5 + ¾ p2q7

6. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Example 2
Polynomial
Degree
Classified by degree
Classified by number of terms -5
¼ x
-9x + 2
x2 – 6
-x3 + 2x + 1
3x4 + 2x3 – x2 + 5x – 8

7. Section 6.2: Polynomials: Classification, Addition, and Subtraction
To add or subtract polynomials, add and subtract the like terms
Same variable, same exponent

8. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Example 3
Find the sum. Write the answer in standard form.
(-8x3 + x – 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3)
(6x2 – x + 3) + (-2x + x2 – 7)

9. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Example 4
Find the difference. Write the answer in standard form.
(-6x3 + 5x – 3) – (2x3 + 4x2 – 3x + 1)
(4x2 – 1) – (3x – 2x2)
(12x – 8x2 + 6) – (-8x2 – 3x + 4)

10. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Example 2
Simplify each expression
(2a3 + 5a – 7) – (a3 – 3a + 2)
(4x2 – 9x + 3) + (-2x2 – 5x – 6)

11. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Example 5
The first floor of a home has the floor plan shown below. Find an expression in standard form for the area of the first floor.

12. Section 6.2: Polynomials: Classification, Addition, and Subtraction
Homework: Practice Exercises
Pg. 262 #2-30 (even), 39, 40