1. ADD AND SUBTRACT
POLYNOMIALS
Chapter 9 section 1

2. Polynomials
A polynomial is a monomial or a sum of monomials, each
called a term of the polynomial.
What is a monomial?
A monomial is a number, a variable, or the product of a
number and one or more variables with whole number
exponents.
15x – x3 + 3
Is a polynomial
A polynomial can be named by its terms or its degree.

3. • A one term polynomial is called a monomial.
• A monomial is a number, a variable, or the product of a
number and one or more variables with whole number
exponents.
• A two term polynomial is called a binomial.
• A binomial is the sum or difference of two monomials.
• A three term polynomial is called a trinomial.
• A trinomial is the sum or difference of three monomials
• More than three terms is just called a polynomial.

4. Degree of a Polynomial
The degree of a polynomial is the greatest degree of its
terms.
Leading coefficient
2x3 + x2 – 5x + 12
Degree Constant term
When a polynomial is written so that the exponents of a
variable decrease from left to right.

5. Terms and Degrees
Is it a polynomial?
Classify by degree and number of terms.
• 15x – x3 + 3
•9
• 2x2 + x – 5
• 6n4 – 8n
• n-2 – 3
• 7bc3 + 4b4c

6. Addition and Subtraction
• Addition
• Combine like terms
• (2x3 – 5x2 + x) + ( 2x2 + x3 –1)
• (3x2 + x – 6) + (x2 + 4x + 10)
• Subtraction
• Add the opposite
• Combine like terms
• (4n2 + 5) – (-2n2 + 2n – 4)
• (4x2 – 3x + 5) – (3x2 – x – 8)

7. MULTIPLY AND DIVIDE
POLYNOMIALS
Chapter 9 section 2

8. Multiplying a monomial by a polynomial
• Use the distributive property.
• 2x3 (x3 + 3x2 – 2x + 5)
• x (7x2 + 4)
• 3x2 (2x3 – x2 + 4x – 3)

9. Multiplying a binomial by a binomial
• FOIL
• First times first
• Outer times outer
• Inner times inner
• Last times last
(x – 4) (3x + 2)

10. Multiplying a binomial by a binomial
• (3a + 4) ( a – 2)
• (4n – 1) (n + 5)

11. Multiplying a binomial by a trinomial
Use the box method
• (2x2 + 5x – 1) (4x – 3)
2x2 5x -1
4x
-3
• Combine like terms

12. Multiplying Polynomials
• (x2 + 2x + 1) (x + 2)
• (3y2 – y + 5) (2y – 3)
• (2x2 – x – 2) (3x – 1)

13. Homework
• Pages 557 – 558
#11-25 odd,
• Pages 565 – 566
#23 - 39 odd