1. 5.3 - Operating Polynomials
Worksheet Key
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5.3 - Operating Polynomials

2. 5.3 - Operating Polynomials
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5.3 - Operating Polynomials

3. Operating Polynomials
Section 5.3
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5.3 - Operating Polynomials

4. 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)
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5.3 - Operating Polynomials

5. 5.3 - Operating Polynomials
Example 1
Add (x2 – 5x + 6) + (3x2 + 4x – 9)
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5.3 - Operating Polynomials

6. 5.3 - Operating Polynomials
Your Turn
Add (3x3 – y + 2x – 5) + (x + y + 5)
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5.3 - Operating Polynomials

7. 5.3 - Operating Polynomials
Example 2
Subtract (x2 – 5x + 6) – (3x2 + 4x – 9)
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5.3 - Operating Polynomials

8. 5.3 - Operating Polynomials
Your Turn
Subtract (7x2 + 4x + 7) – (–8x + 2)
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5.3 - Operating Polynomials

9. 5.3 - Operating Polynomials
Example 3
Multiply 5x(2x3 + 6)
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5.3 - Operating Polynomials

10. 5.3 - Operating Polynomials
Your Turn
Multiply –5x3(2x2 – 9x + 2)
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5.3 - Operating Polynomials

11. 5.3 - Operating Polynomials
Example 4
Multiply (x + 2)(x + 3)
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5.3 - Operating Polynomials

12. 5.3 - Operating Polynomials
Example 5
Multiply (4x + 3)(3x – 5)
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5.3 - Operating Polynomials

13. 5.3 - Operating Polynomials
Your Turn
Multiply (x4 + 2)(3x2 – 1)
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5.3 - Operating Polynomials

14. 5.3 - Operating Polynomials
Review
Add (x – 3) + (–x2 + 2x + 4)
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5.3 - Operating Polynomials

15. Example 6 (using Distribution)
Multiply (x – 3)(–x2 + 2x + 4)
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5.3 - Operating Polynomials

16. 5.3 - Operating Polynomials
Example 6 (using Box)
Multiply (x – 3)(–x2 + 2x + 4)
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5.3 - Operating Polynomials

17. 5.3 - Operating Polynomials
Example 7
Multiply (x + 2)(3x2 – 4x + 1)
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5.3 - Operating Polynomials

18. 5.3 - Operating Polynomials
Your Turn
Multiply (2x3 – 3x + 4)(x2 + 1)
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5.3 - Operating Polynomials

19. 5.3 - Operating Polynomials
Example 8
Multiply (x – 5)(x + 1)(x + 3)
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5.3 - Operating Polynomials

20. 5.3 - Operating Polynomials
Example 8
Multiply (x – 5)(x + 1)(x + 3)
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5.3 - Operating Polynomials

21. 5.3 - Operating Polynomials
Your Turn
Multiply (2x + 1)(3x – 2)(4x – 3)
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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
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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
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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 5 1
(x + y)5 =
x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5 1 5 10 10
Row 5
(x + y)5
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5.3 - Operating Polynomials

25. 5.3 - Operating Polynomials
Example 9
Multiply (x + y)4 1 2 3 4 6 5 10
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5.3 - Operating Polynomials

26. 5.3 - Operating Polynomials
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
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5.3 - Operating Polynomials

27. 5.3 - Operating Polynomials
Example 10
Multiply (x – 5)3
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5.3 - Operating Polynomials

28. 5.3 - Operating Polynomials
Example 11
Multiply (2x – 1)3
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5.3 - Operating Polynomials

29. 5.3 - Operating Polynomials
Your Turn
Multiply (3x – 4)3
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5.3 - Operating Polynomials

30. 5.3 - Operating Polynomials
Assignment
Worksheet
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5.3 - Operating Polynomials