1. ZEROS=ROOTS=SOLUTIONS Equals x intercepts

3. Another Memory slide

4. Looking for two numbers that add to column A and Multiply to column B 7 6 8 -3 -5 13 1 -4 12 8 -9 -10 6 30 -2 4 3 and 4 4 and 2 9 and -1 -5 and 2 -3and -2 3 and 10 2 and -1 -2 and -2 A B

5. Polynomials Defining Polynomials Adding Like Terms

6. Monomials - a number, a variable, or a product of a number and one or more variables. 4x, 20x 2 yw 3, -3, a 2 b 3, and 3yz are all monomials. Polynomials – one or more monomials added or subtracted 4x + 6x 2, 20xy - 4, and 3a 2 - 5a + 4 are all polynomials. Vocabulary

7. Like Terms Like Terms refers to monomials that have the same variable(s) but may have different coefficients. The variables in the terms must have the same powers. Which terms are like? 3a 2 b, 4ab 2, 3ab, -5ab 2 4ab 2 and -5ab 2 are like. Even though the others have the same variables, the exponents are not the same. 3a 2 b = 3aab, which is different from 4ab 2 = 4abb.

8. Like Terms Constants are like terms. Which terms are like? 2x, -3, 5b, 0 -3 and 0 are like. Which terms are like? 3x, 2x 2, 4, x 3x and x are like. Which terms are like? 2wx, w, 3x, 4xw 2wx and 4xw are like.

9. Add: (x 2 + 3x + 1) + (4x 2 +5) Step 1: Underline like terms: Step 2: Add the coefficients of like terms, do not change the powers of the variables: Adding Polynomials (x 2 + 3x + 1) + (4x 2 +5) Notice: ‘3x’ doesn’t have a like term. (x 2 + 4x 2 ) + 3x + (1 + 5) 5x 2 + 3x + 6

10. Adding Polynomials Add the following polynomials; you may stack them if you prefer:

11. Subtract: (3x 2 + 2x + 7) - (x 2 + x + 4) Subtracting Polynomials Step 1: Change subtraction to addition ( Keep-Change-Change. ). Step 2: Underline OR line up the like terms and add. (3x 2 + 2x + 7) + (- x 2 + - x + - 4) (3x 2 + 2x + 7) + (- x 2 + - x + - 4) 2x 2 + x + 3

12. Subtracting Polynomials Subtract the following polynomials by changing to addition (Keep-Change-Change.), then add:

14. WHEN MULTIPLYING LIKE BASES, YOU ADD THE EXPONENTS FOR EXAMPLE: NOW YOU TRY:

16. x2x2 -5x+4 2x -5 5) Multiply (2x - 5)(x 2 - 5x + 4) You cannot use FOIL because they are not BOTH binomials. You must use the distributive property or box method. 2x 3 -5x 2 -10x 2 +25 x +8x -20 Almost done! Go to the next slide!

17. x2x2 -5x+4 2x -5 5) Multiply (2x - 5)(x 2 - 5x + 4) Combine like terms! 2x 3 -5x 2 - 10x 2 +25 x +8x -20 2x 3 – 15x 2 + 33x - 20

20. #1 Divide a polynomial by a monomial.

21. WHEN DIVIDING LIKE BASES, YOU SUBTRACT THE EXPONENTS. FOR EXAMPLE: NOW YOU TRY:

22. #2 Divide a polynomial by a monomial.

23. #3 Divide the following numbers. Check

24. Long Division 1. Divide the first term of the numerator by the first term of the denominator. 2. Distribute your quotient by the entire polynomial in the denominator. 3. Distribute a negative by through your product.

25. #4 Divide the following numbers (Long Division) Remainder

26. #5 Dividing a polynomial by a polynomial (Long Division) Check

27. POLYNOMIALS – DIVIDING EX – Long division (5x³ -13x² +10x -8) / (x-2) 5x³ - 13x² + 10x - 8x - 2 5x² 5x³ - 10x²-() -3x²+ 10x - 3x -3x² + 6x - () 4x - 8 4x - 8 - () + 4 0 R 0

28. #6 Dividing a polynomial by a polynomial (Long Division) Check

29. #7 Dividing a polynomial by a polynomial (Long Division)

30. #8 Dividing a polynomial by a polynomial (Long Division)