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11. 1 Multiplying a Monomial by a Polynomial

11. 1 Multiplying a Monomial by a Polynomial. NOTES. EXAMPLES. MULTIPLYING A MONOMIAL BY A POLYNOMIAL. monomial- no + or - signs ex/ 5x 2 y 3 b inomial- ONLY 1 + or - sign ex/ 5x 3 +3y t rinomial- ONLY 2 + and/or - signs ex/ 7x 2 +6x+4 p olynomial- 3 or more +/- signs

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11. 1 Multiplying a Monomial by a Polynomial

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  1. 11. 1 Multiplying a Monomial by a Polynomial

  2. NOTES EXAMPLES

  3. MULTIPLYING A MONOMIAL BY A POLYNOMIAL monomial- no + or - signs ex/ 5x2y3 binomial- ONLY 1 + or - sign ex/ 5x3+3y trinomial- ONLY 2 + and/or - signs ex/ 7x2+6x+4 polynomial- 3 or more +/- signs ex/ 5x2+y2+3x+2y-7 STEPS: To distribute term outside ( ) to every term inside ( ) do the following: 1. Multiply the # outside ( ) by each # of each term inside ( ) 2. Add the exponents of the variables in every term outside ( ) to the same variables in every term inside ( ) 3. Write your answer in standard form (put terms in order from highest to lowest

  4. C B A A

  5. 2a(a2-3a+1) C -3x3(2x4-x2-8) B 1 x3(8x2+12x-4) 4 A 1 x2y(4x+2xy-8y) 2 A

  6. BELLWORK 1. 3x (4x2 - 3x + 2) 2. -b4 (4b3 + b2 - 2b) 3. 12a2b (2ab2 + 1a - 3b)

  7. 11. 2 Multiplication of Binomials (baby bear - c levels)

  8. NOTES EXAMPLES

  9. MULTIPLICATION OF BINOMIALS BOX MODEL: (x+3)(2x-4) F.O.I.L: First Outer Inner Last (x+3)(2x-4) (2x-4)(x+3)

  10. Examples: C C C

  11. Examples: (2a-5)(a+4) C (x-8)(3x-4) C (2m2-6m)(m+2) C

  12. BELLWORK

  13. 11. 3 F.O.I.L. (mama bear - b levels)

  14. PLUS/MINUS SQUARING

  15. FOIL (Special Cases) SQUARING BINOMIALS: - When given a binomial squared, you must re-write to FOIL ex/ (3x-2)2 ex/ (4x+3)2 B B

  16. Plus/Minus: - FOIL just like always :-) BUT - notice a pattern that the middle term will cancel out ex/ (x-2)(x+2) ex/ (3a2+j)(3a2-j) B B B

  17. BELLWORK

  18. 11. 4 Multiplying Polynomials (papa bear - a levels)

  19. NOTES & EX #1 EX # 2 & EX # 3

  20. Multiplying Polynomials Each term from the first binomial should multiply to each term of the trinomial. Ex1: (2x2-1)(4x2-3x+2) A Box Method:

  21. A Ex2: (4x2+5)(2x2-5x+1) Ex3: 3x4+(2x2-6)2 In HW

  22. BELLWORK

  23. 11. 5 Factoring the Greatest Common Factor

  24. Factoring a Polynomial Finding the GCF

  25. FINDING THE GREATEST COMMON FACTOR Finding the GCF: 1. 12, 6 2. 9x2, 15x 3. 30x4, 6x6, 18x2 4. x5y3, x8y2 5. 10a3b4c, 5ab3, 20a2b

  26. Factoring a Polynomial: 1. 7x-14 2. 16x-8 3. 5x3+10x2-15x 4. 22x3+x5+14x7 5. 28x2y+14xy2-7xy C C B B A

  27. BELLWORK

  28. 11. 6 Solving by Factoring Out the Greatest Common Factor

  29. NOTES & EX 1 Examples

  30. Solving By Factoring Out the Greatest Common Factor STEPS: 1. Set the equation equal to 0 2. Find the factors & GCF 3. Set each factor equal to 0 and solve Ex1: 3x-6=0 C

  31. C B A

  32. Ex2: 2x+10=0 C Ex3: 3x2-6x=0 B Ex4: -4x2=12x A

  33. BELLWORK

  34. 11. 7 Factor and Solving Trinomials (Quadratics) 11. 8 Factor and Solve Special Trinomials

  35. NOTES & EX 1 Examples

  36. Factoring & Solving Trinomials (Quadratics) STEPS: 1. Factor out the GCF if there is one 2. Factor the trinomial using factors of "c" that have a sum of "b" 3. Write as 2 binomials & FOIL to check answer 4. Set each binomial equal to 0 and solve. Ex 1: x2+9x+18

  37. B,C B,C A

  38. Ex 2: x2+25x+24 B,C Ex 3: x2-11x+30 B,C Ex 4: 5x2-30x+45 A

  39. BELLWORK

  40. 11. 8 Factor and Solve Special Trinomials

  41. B Levels A Levels FOLDED PAPER INSERT (C Levels) STAPLE

  42. C-Level Paper Examples

  43. Factoring & Solve Special Trinomials FACTOR & SOLVE: (B Level) 1. 25x2-4=0 2. 16x2-81=0 3. 4x2-16=0 5. 9x2-81=0

  44. A Level The area of a rectangle is represented by x2-169 a) Write the expression for the length & width of the rectangle. L = W = b) If x=16 ft, what is L & W? L= W= L W

  45. BELLWORK

  46. 11.9 Factor and Solve by Grouping

  47. Ex 1 Ex 2 & Ex 3 FOLDED PAPER INSERT (Steps) STAPLE

  48. Steps: (For polynomials with 4 terms, do not combine the like terms)

  49. Factor & Solve by Grouping 1. 4x2+12x-x-3=0

  50. 2. 2x2+9x+5x+20=0 3. 9x2+36x-6x-24=0

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