of 36

# POLYNOMIAL NOTES Day #2

Day 2
Published on: Mar 4, 2016
Published in: Education

#### Transcripts - POLYNOMIAL NOTES Day #2

• 1. Combine Like Terms 1) 3x – 6 + 2x – 8 2) 3x – 7 + 12x + 10 3) 10xy + 5y – 6xy – 14y 5x – 14 15x + 3 4xy – 9y Warm up
• 2. PolynomialPolynomial Operations &Operations & RulesRules
• 3. VOCABULARYVOCABULARY
• 4. Degree The exponent for a variable
• 5. Degree of the Polynomial Highest (largest) exponent of the polynomial
• 6. Standard Form Terms are placed in descending order by the DEGREE
• 7. Leading Coefficient Once in standard form, it’s the 1st NUMBER in front of the variable (line leader)
• 8. # of Terms Name by # of Terms 1 Monomial 2 Binomial 3 Trinomial 4+ Polynomial
• 9. Degree (largest exponent) Name by degree 0 Constant 1 Linear 2 Quadratic 3 Cubic
• 10. 2 9y− + Special Names: Linear Binomial Degree Name: # of Terms Name: Leading Coefficient: -2
• 11. 3 34x Special Names: Cubic Monomial Degree Name: # of Terms Name:
• 12. 2 4 6x x+ Special Names: Quadratic Binomial Degree Name: # of Terms Name: Leading Coefficient: 4
• 13. 3 2 7 2y y y+ − Special Names: Cubic Trinomial Degree Name: # of Terms Name: Leading Coefficient: 1
• 14. Adding Polynomials
• 15. ( ) ( )2 2 2 4 3 5 1x x x x− + + + − 1. 3x2 + x + 2
• 16. ( ) ( )2 6 2 8x x+ + − 2. x2 + 2x – 2
• 17. Subtracting Polynomials
• 18. When SUBTRACTING polynomials Drop the 1st parenthesis then distribute the NEGATIVE to the 2nd parenthesis.
• 19. ( ) ( )2 2 3 10 8a a a a+ − − 3a2 + 10a – 8a2 + a – 5a2 + 11a 3.
• 20. ( ) ( )2 2 3 2 4 2 1x x x x+ − − + − 3x2 + 2x – 4 – 2x2 – x + 1 x2 + x – 3 4.
• 21. PRACTICE
• 23. Multiplying Polynomials
• 24. The Distributive Property Look at the following expression: 3(x + 7) This expression is the sum of x and 7 multiplied by 3. To simplify this expression we can distribute the multiplication by 3 to each number in the sum. (3 • x) + (3 • 7) 3x + 21
• 25. Multiply: (x + 2)(x – 5) Though the format does not change, we must still distribute each term of one polynomial to each term of the other polynomial. Each term in (x+2) is distributed to each term in (x – 5).
• 26. (x + 2)(x – 5) This pattern for multiplying polynomials is called FOIL. Multiply the First terms. Multiply the Outside terms. Multiply the Inside terms. Multiply the Last terms. F O I L After you multiply, collect like terms.
• 27. Example: (x – 6)(2x + 1) x(2x) + x(1) – (6)2x – 6(1) 2x2 + x – 12x – 6 2x2 – 11x – 6
• 28. -2x(x2 – 4x + 2) 3 2 2 8 4x x x− + − 5.
• 29. (x + 3) (x – 3)6.
• 30. (3x – 1)(2x – 4) 2 6 14 4− +x x 7.
• 31. 8. Find the area of the rectangle. 2 28 96 80+ +x x 7 10+x 4 8+x
• 32. 9. Find the volume. 3 2 9 18+ +x x x 3+x 6+x x
• 33. PRACTICE
• 35. MORE PRACTICE…YAY!
• 36. ANSWERS #2