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Algebra Review

Algebra Review. Warm-up (3 m). Multiply: 1. 4x 2 (7x 3 - 6x 2 + 12x - 10) 2. (3x 2 - 5)(x + 4) Factor: 3. x 3 – 64x 4. 9x 2 – 9x – 4. We’re going to review the following skills for the next unit:. Multiplying Polynomials Factoring Polynomials

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Algebra Review

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  1. Algebra Review

  2. Warm-up (3 m) • Multiply: 1. 4x2(7x3 - 6x2 + 12x - 10) 2. (3x2 - 5)(x + 4) • Factor: 3. x3 – 64x 4. 9x2 – 9x – 4

  3. 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

  4. Multiplying Polynomials Distribute FOIL First – Outer – Inner – Last (3x + 5)(x – 7) • Multiply each term inside the parentheses by the term outside the parentheses. 3x5(x7 – 2x4 + 11x)

  5. Multiplying Polynomials, cont. Vertical Multiplication • Works well when you multiply anything larger than a binomial and a binomial. • Example: (3x2 – x + 1)(x2 + 2x – 3) • Very similar to long multiplication by hand.

  6. Example • (7x2 – 5x +6)(2x – 1)

  7. Example • (3x2 – x + 1)(x2 + 2x – 3)

  8. Multiplying with Trigonometric Functions • Exactly the same as multiplying without trigonometric functions.

  9. Your Turn: • Multiply problems 1 – 10 in the Algebra Review packet

  10. 1. 2. 3. 4. 5.

  11. 6. 7. 8. 9. 10.

  12. 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

  13. Leading Coefficient = 1 x2 – 7x + 10

  14. Leading Coefficient ≠ 1 3x2 – 11x – 20

  15. Greatest Common Factor 4x4 – 40x3 + 8x2

  16. Difference of Squares 81x4 – 100

  17. Factoring with Trigonometric Functions • Exactly the same as factoring without trigonometric functions.

  18. Your Turn: • Factor problems 11 – 24 in the Algebra Review packet.

  19. 11. 12. 13. 14. 15. 16.

  20. 17. 18. 19. 20. 21. 22.

  21. 23. 24.

  22. Warm-up (3 m) 1. Multiply: 2. Factor: • Find the reciprocals of the numbers below: 3. 4. 7

  23. Seek and Solve!!! Show all your work on a piece of paper. I’m collecting it for a classwork grade.

  24. Simplifying Rational Expressions • You can only cancel factors that are separated by multiplication!!! Wrong!!! Right!!!

  25. Simplifying Rationals, cont. • You can also reduce factors – as long as they’re separated by multiplication.

  26. Simplifying Rationals, cont. • Factor the numerator and the denominator • Optional – Identify the factors in the numerator and the denominator. • Cancel common factors in the numerator and the denominator.

  27. Example Factors in Numerator Factors in Denominator

  28. Example Factors in Numerator Factors in Denominator

  29. 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.

  30. 25. 26. 27. 28.

  31. 29. 30. 31. 32.

  32. Warm-up (3 m) • Simplify:

  33. Homework Review

  34. Multiplying Rational Expressions • Factor the numerator and the denominator. • Cancel and/or cross cancel any common factors that are separated by multiplication. • Optional – Rewrite the simplified fractions. • Multiply across. (Multiply the numerators together and the denominators together.)

  35. Example

  36. Example

  37. Your Turn • Multiply problems 33 – 38 in the Algebra Review packet. Simplify your answers.

  38. 33. 34. 35. 36. 37. 38.

  39. What About…?

  40. Dividing Rational Expressions • Division is the same thing as multiplication by the reciprocal!

  41. Dividing Rationals, cont. • Rewrite the division as multiplication by the reciprocal. • Factor the numerator and the denominator. • Cancel and/or cross cancel any common factors separated by multiplication. • Multiply across.

  42. Example

  43. Example

  44. Your Turn: • Divide problems 39 – 48 in the Algebra Review packet.

  45. 39. 40. 41. 42.

  46. 43. 44. 45. 46.

  47. 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.

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