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Algebra

Algebra. 10.2 Multiplying Polynomials. Consider a rectangular house. It is 12 feet wide by 18 feet long . OK...... it’s a small house. 18. 12. What is the area of this small house?. 12. 18. x 18. 216. 12. It is 216 square feet.

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Algebra

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  1. Algebra 10.2 Multiplying Polynomials

  2. Consider a rectangular house It is 12 feet wide by 18 feet long OK...... it’s a small house....... 18 12

  3. What is the area of this small house? 12 18 x 18 216 12 It is 216 square feet.

  4. Let’s add interior walls to the house to make 4 rooms 18 10 8 10 12 2

  5. What is the square footage of each room? Does it still add up to 216 ? 18 10 8 100 80 20 10 100 80 16 12 216 2 20 16 YES

  6. So the total product is equal to the sum of the smaller products. 18 10 8 100 80 12 20 10 x 18 100 80 16 12 = 216 216 2 20 16

  7. ….and we can multiply the dimensions horizontally like this…. (10 + 8) (10 + 2) 18 10 8 20 + 80 + 16 100 + 10 100 80 12 = 216 2 20 16

  8. Let’s do something “crazy” and say that 10 = x. x + 8 x 8 x x² 8x x + 2 2 2x 16

  9. ….and we can multiply the dimensions horizontally like this…. Put the 10 back for x and check (x + 8) ( x + 2) x + 8 x 8 2x + 8x + 16 x² + x x² 8x = x² + 10x + 16 x + 2 = (10)² + 10(10) + 16 2 2x 16 = 216

  10. MultiplyingPolynomials When multiplying polynomials, you use the distributive property. Each term in one polynomial gets multiplied by each term in the other polynomial. When a binomial is multiplied by another binomial, we refer to the pattern as “FOIL”

  11. FOIL Stands for: (x + 8) ( x + 2) First Outside Inside Last x² 2x 8x 16 + + + = x² + 10x + 16

  12. Try these x²+ 4x - 21 (x + 7) (x – 3) 3x²- 11x - 20 (3x + 4)(x – 5) (2x – 5)(x – 3) 2x²- 11x + 15 (x + 3)(x – 3) x²- 9

  13. It works the same for multiplying binomials by other polynomials. (3x + 2)(x² – 5x + 3) 3x³- 15x² + 9x + 2x²- 10x + 6 When you multiply a 2 by 3 you get 2 x 3 = 6 terms 3x³- 13x²- x + 6 Then combine like terms

  14. Homework pg. 587 # 19 - 47 odd, 54-55, 62-73

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