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
PolynomialPolynomial
Operations &Operations &
RulesRules
VOCABULARYVOCABULARY
Degree
The exponent for a
variable
Degree of the Polynomial
Highest (largest)
exponent of the
polynomial
Standard Form
Terms are placed in
descending order
by the DEGREE
Leading Coefficient
Once in standard
form, it’s the 1st
NUMBER in front of the
variable (line leader)
# of
Terms
Name by # of
Terms
1 Monomial
2 Binomial
3 Trinomial
4+ Polynomial
Degree
(largest exponent)
Name by
degree
0 Constant
1 Linear
2 Quadratic
3 Cubic
2 9y− +
Special Names:
Linear
Binomial
Degree Name:
# of Terms Name:
Leading Coefficient:
-2
3
34x
Special Names:
Cubic
Monomial
Degree Name:
# of Terms Name:
2
4 6x x+
Special Names:
Quadratic
Binomial
Degree Name:
# of Terms Name:
Leading Coefficient: 4
3 2
7 2y y y+ −
Special Names:
Cubic
Trinomial
Degree Name:
# of Terms Name:
Leading Coefficient: 1
Adding
Polynomials
( ) ( )2 2
2 4 3 5 1x x x x− + + + −
1.
3x2
+ x + 2
( ) ( )2
6 2 8x x+ + −
2.
x2
+ 2x – 2
Subtracting
Polynomials
When SUBTRACTING polynomials
Drop the 1st
parenthesis then
distribute the NEGATIVE to the 2nd
parenthesis.
( ) ( )2 2
3 10 8a a a a+ − −
3a2
+ 10a – 8a2
+ a
– 5a2
+ 11a
3.
( ) ( )2 2
3 2 4 2 1x x x x+ − − + −
3x2
+ 2x – 4 – 2x2
– x + 1
x2
+ x – 3
4.
PRACTICE
ANSWERS
Multiplying
Polynomials
The Distributive Property
Look at the following expression:
3(x + 7) This expression is the sum of x and 7 multiplied by 3...
Multiply: (x + 2)(x – 5)
Though the format does not change, we must still distribute each term of one
polynomial to each t...
(x + 2)(x – 5)
This pattern for multiplying polynomials is called FOIL.
Multiply the First terms.
Multiply the Outside ter...
Example: (x – 6)(2x + 1)
x(2x) + x(1) – (6)2x – 6(1)
2x2
+ x – 12x – 6
2x2
– 11x – 6
-2x(x2
– 4x + 2)
3 2
2 8 4x x x− + −
5.
(x + 3) (x – 3)6.
(3x – 1)(2x – 4)
2
6 14 4− +x x
7.
8. Find the area of the rectangle.
2
28 96 80+ +x x
7 10+x
4 8+x
9. Find the volume.
3 2
9 18+ +x x x
3+x
6+x
x
PRACTICE
ANSWERS
MORE PRACTICE…YAY!
ANSWERS #2
of 36

POLYNOMIAL NOTES Day #2

Day 2
Published on: Mar 4, 2016
Published in: Education      
Source: www.slideshare.net


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
  • 22. ANSWERS
  • 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
  • 34. ANSWERS
  • 35. MORE PRACTICE…YAY!
  • 36. ANSWERS #2