1. An Introduction to Polynomials Copyright Scott Storla 2015

2. Some Vocabulary for Polynomials Copyright Scott Storla 2015

3. Coefficient Variable termConstant term Copyright Scott Storla 2015

5. Special names for the number of terms. Copyright Scott Storla 2015

6. 1.Write the polynomial as a sum with all coefficients and exponents explicit. 2.Discuss the polynomial in both general and specific terms.

7. Copyright Scott Storla 2015 1.Write the polynomial as a sum with all coefficients explicit. 2.Discuss the polynomial in both general and specific terms.

8. The degree of a term The degree of the entire polynomial is the same as the degree of the term with the largest exponent. Copyright Scott Storla 2015 The degree of a polynomial For each variable term use the exponent to decide on the degree of the term.

9. Standard Form The terms of the polynomial are written in decreasing order of degree from left to right. Copyright Scott Storla 2015 To write a polynomial in standard form we imagine all operations are addition and all coefficients are explicit, then we use the commutative property to rearrange the terms, last we rewrite all explicit coefficients implicitly.

10. Standard Form In practice people rearrange the terms of a polynomial “in their head”. Copyright Scott Storla 2015 Write each polynomial in standard form.

11. Copyright Scott Storla 2015 1.Write the polynomial in standard form 2.Discuss the polynomial in general terms. 3.Discuss the polynomial term by term.

12. Copyright Scott Storla 2015 1.Write the polynomial in standard form 2.Discuss the polynomial in general terms. 3.Discuss the polynomial term by term.

13. Multivariable or “mixed” terms With multivariable terms the degree of the term is the sum of the individual exponents. We don’t actually add the exponents. Copyright Scott Storla 2015

14. Multivariable or “mixed” terms Copyright Scott Storla 2015 For standard form, terms of equal degree can be written in any order but often decisions are made using alphabetical order.

15. Copyright Scott Storla 2015 1.Write the polynomial in standard form 2.Discuss the polynomial in general terms. 3.Discuss the polynomial term by term.

16. Copyright Scott Storla 2015

17. Some Vocabulary for Polynomials Copyright Scott Storla 2015

18. Adding and Subtracting Polynomials Copyright Scott Storla 2015

19. Terms are like if, in general, they’re counting the same sized unit. Copyright Scott Storla 2015 Only like terms can be added or subtracted.

20. Like Polynomial Terms Copyright Scott Storla 2015 Polynomial terms in one variable are like if the variable has the same exponent. Constant terms are also considered like.

21. Decide on the like terms Copyright Scott Storla 2015

22. Simplify Copyright Scott Storla 2015

23. Simplify Copyright Scott Storla 2015

24. Simplify Copyright Scott Storla 2015

25. Simplify Copyright Scott Storla 2015

26. Adding and Subtracting Polynomials Copyright Scott Storla 2015