3. Section 7.3 Products and Factors of Polynomials

4. Factoring the Sum and Difference of Two Cubes

5. Factor Theorem (x-r) is a factor of the polynomial expression that defines the function P if and only if r is a solution of P(x) = 0, that is, if and only if P(r) = 0. In other words: – Set x-r = 0 – Solve for x. x = r – Plug this r in for every x in the original polynomial – Simplify – If you get 0 then (x – r) IS a factor of the polynomial

9. Let’s look at how to do this using the example: In order to use synthetic division these two things must happen: There must be a coefficient for every possible power of the variable. The divisor must have a leading coefficient of 1. #1#2

10. Step #1: Write the terms of the polynomial so the degrees are in descending order.

11. Step #2: Write the constant a of the divisor x- a to the left and write down the coefficients.

12. Step #3: Bring down the first coefficient, 5.

13. Step #5: After multiplying in the diagonals, add the column. Add the column

14. Multiply the diagonals, add the columns. Add 15*3 = 45

15. Step #7: Repeat the same procedure as step #6. Add Columns

16. The quotient is: Remember to place the remainder over the divisor.

17. Step #8: Write the quotient. The numbers along the bottom are coefficients of the power of x in descending order, starting with the power that is one less than that of the dividend.

23. Divide a polynomial by a monomial.

25. Divide the following numbers. Check

26. Divide the following numbers (Long Division) Remainder

27. Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

28. Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

29. Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

30. Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

31. Dividing a polynomial by a polynomial (Long Division) NOW YOU WRITE THIS ONE

32. Dividing a polynomial by a polynomial (Long Division)

33. NOW YOU WRITE THIS ONE

34. Dividing a polynomial by a polynomial (Long Division)

38. Homework Problems 1. 2. 3. 4.