1. Warm Up Multiply: 1. 4x 2 (7x 3 - 6x 2 + 12x - 10) 2. (3x 2 - 5)(x + 4) Factor: 3. x 3 – 64x4. 9x 2 – 9x – 4 EQ: How do I perform algebraic operations involving trigonometric expressions?

2. We’re going to review the following skills for the next unit: Multiplying Polynomials Factoring Polynomials Simplifying Rational Expressions Multiplying Rational Expressions Dividing Rational Expressions Adding and Subtracting Rational Expressions EQ: How do I perform algebraic operations involving trigonometric expressions?

3. Multiplying Polynomials Distribute Multiply each term inside the parentheses by the term outside the parentheses. 3x 5 (x 7 – 2x 4 + 11x) FOIL First – Outer – Inner – Last (3x + 5)(x – 7) EQ: How do I perform algebraic operations involving trigonometric expressions?

4. Multiplying Polynomials, cont. Works well when you multiply anything larger than a binomial and a binomial. – Example: (3x 2 – x + 1)(x 2 + 2x – 3) Very similar to long multiplication by hand. Vertical Multiplication EQ: How do I perform algebraic operations involving trigonometric expressions?

5. Example (7x 2 – 5x +6)(2x – 1) EQ: How do I perform algebraic operations involving trigonometric expressions?

6. Example (3x 2 – x + 1)(x 2 + 2x – 3) EQ: How do I perform algebraic operations involving trigonometric expressions?

7. Multiplying with Trigonometric Functions Exactly the same as multiplying without trigonometric functions. EQ: How do I perform algebraic operations involving trigonometric expressions?

8. Your Turn: Multiply problems 1 – 10 in the Algebra Review packet EQ: How do I perform algebraic operations involving trigonometric expressions?

9. Factoring Remember, there are four types of factoring that we reviewed at the beginning of the semester: – Leading Coefficient = 1 (“Regular” Factoring) – Leading Coefficient ≠ 1 (Box Method or Welsh Method) – Greatest Common Factor (GCF) – Difference of Squares EQ: How do I perform algebraic operations involving trigonometric expressions?

10. Leading Coefficient = 1 x 2 – 7x + 10 EQ: How do I perform algebraic operations involving trigonometric expressions?

11. Leading Coefficient ≠ 1 3x 2 – 11x – 20 EQ: How do I perform algebraic operations involving trigonometric expressions?

12. Greatest Common Factor 4x 4 – 40x 3 + 8x 2 EQ: How do I perform algebraic operations involving trigonometric expressions?

13. Difference of Squares 81x 4 – 100 EQ: How do I perform algebraic operations involving trigonometric expressions?

14. Factoring with Trigonometric Functions Exactly the same as factoring without trigonometric functions. EQ: How do I perform algebraic operations involving trigonometric expressions?

15. Your Turn: Factor problems 11 – 24 in the Algebra Review packet. EQ: How do I perform algebraic operations involving trigonometric expressions?

16. 1. Multiply:2. Factor: Find the reciprocals of the numbers below: 3. 4. 7 EQ: How do I perform algebraic operations involving trigonometric expressions?

17. Simplifying Rational Expressions You can only cancel factors that are separated by multiplication!!! Wrong!!! Right!!! EQ: How do I perform algebraic operations involving trigonometric expressions?

18. Simplifying Rationals You can also reduce factors – as long as they’re separated by multiplication. EQ: How do I perform algebraic operations involving trigonometric expressions?

19. Simplifying Rationals 1.Factor the numerator and the denominator 2.Optional – Identify the factors in the numerator and the denominator. 3.Cancel common factors in the numerator and the denominator. EQ: How do I perform algebraic operations involving trigonometric expressions?

20. Example Factors in Numerator Factors in Denominator EQ: How do I perform algebraic operations involving trigonometric expressions?

21. Example Factors in Numerator Factors in Denominator EQ: How do I perform algebraic operations involving trigonometric expressions?

22. Example Factors in Numerator Factors in Denominator EQ: How do I perform algebraic operations involving trigonometric expressions?

23. Your Turn: Simplify problems 25 – 32 in the Algebra Review packet. Remember to factor the numerator and the denominator first, AND you can only cancel factors separated by multiplication. EQ: How do I perform algebraic operations involving trigonometric expressions?

24. Multiplying Rational Expressions 1.Factor the numerator and the denominator. 2.Cancel and/or cross cancel any common factors that are separated by multiplication. 3.Optional – Rewrite the simplified fractions. 4.Multiply across. (Multiply the numerators together and the denominators together.) EQ: How do I perform algebraic operations involving trigonometric expressions?

25. Example EQ: How do I perform algebraic operations involving trigonometric expressions?

26. Example EQ: How do I perform algebraic operations involving trigonometric expressions?

27. Example EQ: How do I perform algebraic operations involving trigonometric expressions?

28. Your Turn Multiply problems 33 – 38 in the Algebra Review packet. Simplify your answers. EQ: How do I perform algebraic operations involving trigonometric expressions?

29. Warm Up 1.Simplify: 2.Multiply: EQ: How do I perform algebraic operations involving trigonometric expressions?

32. Dividing Rational Expressions Division is the same thing as multiplication by the reciprocal! EQ: How do I perform algebraic operations involving trigonometric expressions?

33. Dividing Rationals 1.Rewrite the division as multiplication by the reciprocal. 2.Factor the numerator and the denominator. 3.Cancel and/or cross cancel any common factors separated by multiplication. 4.Multiply across. EQ: How do I perform algebraic operations involving trigonometric expressions?

34. Example EQ: How do I perform algebraic operations involving trigonometric expressions?

35. Example EQ: How do I perform algebraic operations involving trigonometric expressions?

36. Your Turn: Divide problems 39 – 48 EQ: How do I perform algebraic operations involving trigonometric expressions?

37. Adding and Subtracting Rational Expressions If the fractions have the same denominator, add or subtract the numerators. (Make sure to distribute the subtraction sign!!!) Simplify the fraction is possible. EQ: How do I perform algebraic operations involving trigonometric expressions?

38. Examples EQ: How do I perform algebraic operations involving trigonometric expressions?

39. Adding and Subtracting Rational Expressions If the fractions have the different denominators, 1.Factor the numerator and the denominator. 2.Simplify each fraction individually if possible. 3.Compare the denominators of each fraction. Identify the “missing” factors from each fraction. (Finding the Least Common Denominator) 4.Multiply each fraction by 1. Rewrite 1 as EQ: How do I perform algebraic operations involving trigonometric expressions?

40. Adding and Subtracting Rational Expressions 5.Multiply across. 6.Combine all fractions into one fraction. 7.Simplify the numerator. 8.Factor the numerator if possible. 9.Simplify/reduce the fraction if possible. EQ: How do I perform algebraic operations involving trigonometric expressions?

41. Example EQ: How do I perform algebraic operations involving trigonometric expressions?

42. Example EQ: How do I perform algebraic operations involving trigonometric expressions?

43. Example EQ: How do I perform algebraic operations involving trigonometric expressions?

44. Your Turn: Add or subtract problems 49 – 62 in the Algebra Review packet. EQ: How do I perform algebraic operations involving trigonometric expressions?