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Operating Polynomials

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Presentation on theme: "Operating Polynomials"— Presentation transcript:

1 Operating Polynomials
Section 5.3 12/5/2018 6:00 PM 5.3 - Operating Polynomials

2 Add/Subtract Polynomials
Keep It Simple, Students Combine like terms when adding or subtracting polynomials Create a table/chart when simplifying polynomials (for the visual learners) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

3 5.3 - Operating Polynomials
Example 1 Add (x2 – 5x + 6) + (3x2 + 4x – 9) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

4 5.3 - Operating Polynomials
Your Turn Add (3x3 – y + 2x – 5) + (x + y + 5) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

5 5.3 - Operating Polynomials
Example 2 Subtract (x2 – 5x + 6) – (3x2 + 4x – 9) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

6 5.3 - Operating Polynomials
Your Turn Subtract (7x2 + 4x + 7) – (–8x + 2) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

7 5.3 - Operating Polynomials
Example 3 Multiply 5x(2x3 + 6) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

8 5.3 - Operating Polynomials
Your Turn Multiply –5x3(2x2 – 9x + 2) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

9 5.3 - Operating Polynomials
Multiplying Factors FOIL Method: Multiply the first term in the first bracket and first term in the second bracket (FIRST) Multiply the first term in the first bracket and second term in the second bracket (OUTER) Multiply the second term in the first bracket and first term in the second bracket (INNER) Multiply the second term in the first bracket and second term in the second bracket (LAST) Simplify the expression 12/5/2018 6:00 PM 5.3 - Operating Polynomials

10 5.3 - Operating Polynomials
Example 4 (using FOIL) Multiply (x + 2)(x + 3) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

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Example 4 (using Box) Multiply (x + 2)(x + 3) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

12 5.3 - Operating Polynomials
Example 5 Multiply (4x + 3)(3x – 5) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

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Your Turn Multiply (x4 + 2)(3x2 – 1) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

14 5.3 - Operating Polynomials
Review Add (x – 3) + (–x2 + 2x + 4) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

15 Example 6 (using Distribution)
Multiply (x – 3)(–x2 + 2x + 4) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

16 5.3 - Operating Polynomials
Example 6 (using Box) Multiply (x – 3)(–x2 + 2x + 4) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

17 5.3 - Operating Polynomials
Example 7 Multiply (x + 2)(3x2 – 4x + 1) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

18 5.3 - Operating Polynomials
Your Turn Multiply (2x3 – 3x + 4)(x2 + 1) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

19 5.3 - Operating Polynomials
Example 8 Multiply (x – 5)(x + 1)(x + 3) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

20 5.3 - Operating Polynomials
Example 8 Multiply (x – 5)(x + 1)(x + 3) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

21 5.3 - Operating Polynomials
Your Turn Multiply (2x + 1)(3x – 2)(4x – 3) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

22 5.3 - Operating Polynomials
Pascal’s Triangle Named after Blaise Pascal, a famous French Mathematician and Philosopher Taken from the Fibonnacci’s sequence Viewed through the process of factoring variable binomials 12/5/2018 6:00 PM 5.3 - Operating Polynomials

23 Steps in Binomial Expansion
Plug the equation using Binomial Theorem, using Pascal’s Triangle to determine the coefficients Follow the countdown method for the parenthesis The coefficients follow Pascal's Triangle The first given number or variable increase left to right The second number or variable decreases left to right Simplify 12/5/2018 6:00 PM 5.3 - Operating Polynomials

24 5.3 - Operating Polynomials
Pascal’s Triangle (x + y)0 = 1 Row 0 (x + y)0 1 (x + y)1 = x + y Row 1 (x + y)1 1 1 (x + y)2 = x2 + 2xy + y2 1 2 1 Row 2 (x + y)2 (x + y)3 = x3 + 3x2y + 3xy2 + y3 1 3 3 1 Row 3 (x + y)3 (x + y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4 1 4 6 4 1 Row 4 (x + y)4 (x + y)5 = x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5 1 5 5 1 10 10 Row 5 (x + y)5 12/5/2018 6:00 PM 5.3 - Operating Polynomials

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Example 9 Multiply (x + y)4 1 2 3 4 6 5 10 12/5/2018 6:00 PM 5.3 - Operating Polynomials

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Example 9 1 1 1 Multiply (x + y)4 1 2 1 1 3 3 1 1 4 6 4 1 1 5 5 1 10 10 4 3 2 2 3 1 4 x + 4 x y 6 x y 4 1 + + x y + y 12/5/2018 6:00 PM 5.3 - Operating Polynomials

27 5.3 - Operating Polynomials
Example 10 Multiply (x – 5)3 12/5/2018 6:00 PM 5.3 - Operating Polynomials

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Example 11 Multiply (2x – 1)3 12/5/2018 6:00 PM 5.3 - Operating Polynomials

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Your Turn Multiply (3x – 4)3 12/5/2018 6:00 PM 5.3 - Operating Polynomials

30 5.3 - Operating Polynomials
Example 12 Mr. Silva manages a manufacturing plant. From 1990 through 2005 the number of units produced (in thousands) can be modeled by N(x) = 2x2 + 2x + 3. The average cost per unit (in dollars) can be modeled by C(x) = –4x2 –.1x + 3. Write a polynomial T(x) that can be used to model the total costs. Total cost is the product of the number of units and the cost per unit. T(x) = N(x)  C(x) 12/5/2018 6:00 PM 5.3 - Operating Polynomials

31 5.3 - Operating Polynomials
Your Turn The number of items is modeled by 0.3x x + 2, and the cost per item is modeled by g(x) = –0.1x2 – 0.3x Write a polynomial c(x) that can be used to model the total cost. Total cost is the product of the number of units and the cost per unit. y = –0.03x4 – 0.1x x2 – 0.1x + 10 12/5/2018 6:00 PM 5.3 - Operating Polynomials

32 5.3 - Operating Polynomials
Assignment Worksheet 12/5/2018 6:00 PM 5.3 - Operating Polynomials


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