1. Polynomials and Factoring
Module 6
Polynomials and Factoring

2. 6.1 – Introduction and review of polynomials

3. Classify polynomials by term and degree

4. Prefixes – Classification by terms
Mono – one term
Bi – two terms
Tri – three terms
Poly – more than three terms (literally means: many)

5. Classification by Degrees
The degree of a polynomial is the SUM of the exponents (including no visible exponents, which is an invisible 1) of the highest term.
Examples:
(2+1 = 3) (3+12 = 15)
(4+2 = 6) (3+3 = 6)

6. Standard Form of a Polynomial
Standard form means that all of the exponents are in DESCENDING order (largest to smallest)

7. 6.2 Operations of polynomials

8. Adding Polynomials Combine like terms (same exponent)
Make sure you keep the sign (+ or -) that is in front of each term

9. Subtracting Polynomials
Distribute the negative to everything in the second set of parentheses
Combine like terms (same exponent)
Make sure you keep the sign (+ or -) that is in front of each term

10. Multiplying Polynomials Monomial by a Polynomial
Distribute the first polynomial to all terms in the parentheses
Multiply the coefficients (big number before the variable) and add the exponents

11. Multiplying Polynomials Binomial by a Binomial
Distribute the first term to all terms in the second parentheses
Distribute the second term to all terms in the second parentheses
Combine like terms

12. Multiplying Polynomials
More terms? Just follow the steps and combine like terms!
Make sure you pay attention to the signs and follow PEMDAS!

13. 6.03 Factoring

14. Factoring out the GCF
Find what number and/or variables ALL of the terms have in common
Divide out the common factor
GCF goes in front of the parentheses, and whatever is left after dividing goes in the parentheses

18. Difference of Squares

19. Perfect Square Trinomial

20. Other special cases