1. 2-1 Operations on Polynomials

2. Refer to the algebraic expression above to complete the following: 1)How many terms are there? 2)Give an example of like terms. 3)Give an example of a coefficient. 4)Give an example of a constant. 5)Simplify the expression.

3. 1)There are 6 terms – a term is a constant or a variable or a product of a constant and a variable separated by + and – signs. 2)-6, 1 and are like terms – terms with the same variable to the same power. 3)2, 7, -5, and -1 are coefficients – when the term contains a number and a variable, the number part is the coefficient. 4)-6 and 1 are constants – a term that does not have a variable.

4. To simplify the expression: Add the coefficients of any like terms. Keep the variable and exponent the same. Write in order with the largest exponent first which is the standard (general form) of a polynomial.

5. An expression formed by adding a finite number of “same base” unlike terms. Example: Exponents must be positive integers (no fractions), there can be no square roots, and no variables in the denominator. - Not a polynomial

6.  The exponent of a term is the degree of the term. Example has a degree of 5 The value of the largest term is the degree of a polynomial. Example has a degree of 3 The leading coefficient is the coefficient of the first term when the polynomial is written in standard form (largest degree first).

7. 1) 2)9 + 3x 3)

13. Drop parentheses and add like terms. Make sure answer is in standard form

14. Line up terms by degree

16. Change the signs of the second polynomial and then add.

19.  If you add or subtract polynomials your answer is also a polynomial.  This means polynomials are “closed” under addition and subtraction.

20. 2(3x – 1) Distributive property

21. If you multiply polynomials you get a polynomial as the answer. Polynomials are “closed” for multiplication!!!

22. Let’s do a very simple one. Polynomials are NOT “closed” for divison!!!

23. (x + 3)(2x – 1)Distributive property (twice) Combine “like” terms

25. Distributive property (twice) Combine “like” terms

26. How do you multiply 2 * 3 * 4 three numbers? 6* 4= 24 OR: 2 * 3 * 4 12 2 *= 24OR: 2 * 3 * 4 8* 3= 24 Pick 2 factors, multiply them to get a product, then multiply the product by the last factor

27. Associative Property: if you have 3 or more factors, pick two, multiply them 1 st 2*3*4 (2*3)*4 (to visually show that we are picking 2, we group, or associate them together with parentheses).

28. (x – 1)(2x + 3)(3x – 2) = ? = [ (x – 1)(2x + 3) ] (3x – 2) How do you multiply three binomials? Pick 2 factors, multiply them to get a product, then multiply the product by the last factor  associative property.

30. Square of a sum. (x + y)(x + y)

31. Square of a difference. (x - y)(x - y)

32. Product of a sum and a difference. (x + y)(x – y)

34. Cube of a sum.

35. Cube of a difference.