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Chapter 9Polynomials
Section 9-1Add and Subtract Polynomials
Essential Questions How do you write polynomials in standard form? How do you add and subtract polynomials? Where you’ll s...
Vocabulary1. Monomial:2. Coefficient:3. Constant:4. Polynomial:5. Term:
Vocabulary1. Monomial: An expression that has one term (a    number, variable, or a combination of both a    number and va...
Vocabulary1. Monomial: An expression that has one term (a    number, variable, or a combination of both a    number and va...
Vocabulary1. Monomial: An expression that has one term (a    number, variable, or a combination of both a    number and va...
Vocabulary1. Monomial: An expression that has one term (a    number, variable, or a combination of both a    number and va...
Vocabulary1. Monomial: An expression that has one term (a    number, variable, or a combination of both a    number and va...
Vocabulary6. Binomial:7. Trinomial:8. Standard Form:9. Like Terms:
Vocabulary6. Binomial: A polynomial with two terms7. Trinomial:8. Standard Form:9. Like Terms:
Vocabulary6. Binomial: A polynomial with two terms7. Trinomial: A polynomial with three terms8. Standard Form:9. Like Terms:
Vocabulary6. Binomial: A polynomial with two terms7. Trinomial: A polynomial with three terms8. Standard Form: When a poly...
Vocabulary6. Binomial: A polynomial with two terms7. Trinomial: A polynomial with three terms8. Standard Form: When a poly...
Example 1 Tell the variable for which the polynomial is          arranged in standard form.                   3           ...
Example 1 Tell the variable for which the polynomial is          arranged in standard form.                   3           ...
Example 1 Tell the variable for which the polynomial is          arranged in standard form.                   3           ...
Example 2              Add the polynomials.          2                           2    a. (2x − 3x + 7) + (−2x − 8) + ( x −...
Example 2              Add the polynomials.          2                             2    a. (2x − 3x + 7) + (−2x − 8) + ( x...
Example 2              Add the polynomials.          2                             2    a. (2x − 3x + 7) + (−2x − 8) + ( x...
Example 2              Add the polynomials.          2                             2    a. (2x − 3x + 7) + (−2x − 8) + ( x...
Example 2              Add the polynomials.          2                             2    a. (2x − 3x + 7) + (−2x − 8) + ( x...
Example 2              Add the polynomials.          2                                 2    a. (2x − 3x + 7) + (−2x − 8) +...
Example 2              Add the polynomials.          2                                    2    a. (2x − 3x + 7) + (−2x − 8...
Example 3Subtract 4x + y from the sum of x + 3y and 8x - 2y.
Example 3Subtract 4x + y from the sum of x + 3y and 8x - 2y.          ( x + 3y ) + (8 x − 2y ) − (4 x + y )
Example 3Subtract 4x + y from the sum of x + 3y and 8x - 2y.          ( x + 3y ) + (8 x − 2y ) − (4 x + y )             x ...
Example 3Subtract 4x + y from the sum of x + 3y and 8x - 2y.          ( x + 3y ) + (8 x − 2y ) − (4 x + y )             x ...
Example 4                     Simplify.            3   2                3   2    a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) ...
Example 4                            Simplify.                3       2               3       2    a. (6 x + 3x − 11x ) + ...
Example 4                            Simplify.                3       2                3       2    a. (6 x + 3x − 11x ) +...
Example 4                            Simplify.                3       2                    3       2    a. (6 x + 3x − 11x...
Example 4                                Simplify.                3       2                        3       2    a. (6 x + ...
Example 4                    Simplify.        2          2       2          2     2   c. ( x y + x − xy ) − (− y + y + xy ...
Example 4                    Simplify.        2          2         2         2       2   c. ( x y + x − xy ) − (− y + y + ...
Example 4                    Simplify.        2          2         2               2       2   c. ( x y + x − xy ) − (− y ...
Homework
Homework               p. 378 #1-39 odd“Deeds, not stones, are the true monuments of the             great.” - John L. Mot...
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Int Math 2 Section 9-1

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Add and Subtract Polynomials

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  • Transcript of "Int Math 2 Section 9-1"

    1. 1. Chapter 9Polynomials
    2. 2. Section 9-1Add and Subtract Polynomials
    3. 3. Essential Questions How do you write polynomials in standard form? How do you add and subtract polynomials? Where you’ll see this: Part-time jobs, travel, geography, modeling
    4. 4. Vocabulary1. Monomial:2. Coefficient:3. Constant:4. Polynomial:5. Term:
    5. 5. Vocabulary1. Monomial: An expression that has one term (a number, variable, or a combination of both a number and variables without any addition or subtraction)2. Coefficient:3. Constant:4. Polynomial:5. Term:
    6. 6. Vocabulary1. Monomial: An expression that has one term (a number, variable, or a combination of both a number and variables without any addition or subtraction)2. Coefficient: The number that is with the variable3. Constant:4. Polynomial:5. Term:
    7. 7. Vocabulary1. Monomial: An expression that has one term (a number, variable, or a combination of both a number and variables without any addition or subtraction)2. Coefficient: The number that is with the variable3. Constant: A number without a variable4. Polynomial:5. Term:
    8. 8. Vocabulary1. Monomial: An expression that has one term (a number, variable, or a combination of both a number and variables without any addition or subtraction)2. Coefficient: The number that is with the variable3. Constant: A number without a variable4. Polynomial: A collection of terms that are combined by addition or subtraction5. Term:
    9. 9. Vocabulary1. Monomial: An expression that has one term (a number, variable, or a combination of both a number and variables without any addition or subtraction)2. Coefficient: The number that is with the variable3. Constant: A number without a variable4. Polynomial: A collection of terms that are combined by addition or subtraction5. Term: Each monomial within a polynomial
    10. 10. Vocabulary6. Binomial:7. Trinomial:8. Standard Form:9. Like Terms:
    11. 11. Vocabulary6. Binomial: A polynomial with two terms7. Trinomial:8. Standard Form:9. Like Terms:
    12. 12. Vocabulary6. Binomial: A polynomial with two terms7. Trinomial: A polynomial with three terms8. Standard Form:9. Like Terms:
    13. 13. Vocabulary6. Binomial: A polynomial with two terms7. Trinomial: A polynomial with three terms8. Standard Form: When a polynomial is written from highest to lowest degree (highest to lowest exponent)9. Like Terms:
    14. 14. Vocabulary6. Binomial: A polynomial with two terms7. Trinomial: A polynomial with three terms8. Standard Form: When a polynomial is written from highest to lowest degree (highest to lowest exponent)9. Like Terms: Terms that have the same variable parts (variables and exponents)
    15. 15. Example 1 Tell the variable for which the polynomial is arranged in standard form. 3 2 a. 2a + 3ab − 4b 3 2 b. 2(a + b) + 3(a + b) − 4(a + b) + 7
    16. 16. Example 1 Tell the variable for which the polynomial is arranged in standard form. 3 2 a. 2a + 3ab − 4b a 3 2 b. 2(a + b) + 3(a + b) − 4(a + b) + 7
    17. 17. Example 1 Tell the variable for which the polynomial is arranged in standard form. 3 2 a. 2a + 3ab − 4b a 3 2 b. 2(a + b) + 3(a + b) − 4(a + b) + 7 (a + b)
    18. 18. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
    19. 19. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
    20. 20. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 3x 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
    21. 21. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 3x −12x 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
    22. 22. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 3x −12x −1 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
    23. 23. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 3x −12x −1 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y ) 2 2 2 2 3x − 4 xy − x + 4 y + 2xy − y
    24. 24. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 3x −12x −1 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y ) 2 2 2 2 3x − 4 xy − x + 4 y + 2xy − y 2 2 2x − 2xy + 3y
    25. 25. Example 3Subtract 4x + y from the sum of x + 3y and 8x - 2y.
    26. 26. Example 3Subtract 4x + y from the sum of x + 3y and 8x - 2y. ( x + 3y ) + (8 x − 2y ) − (4 x + y )
    27. 27. Example 3Subtract 4x + y from the sum of x + 3y and 8x - 2y. ( x + 3y ) + (8 x − 2y ) − (4 x + y ) x + 3y + 8 x − 2y − 4 x − y
    28. 28. Example 3Subtract 4x + y from the sum of x + 3y and 8x - 2y. ( x + 3y ) + (8 x − 2y ) − (4 x + y ) x + 3y + 8 x − 2y − 4 x − y 5x
    29. 29. Example 4 Simplify. 3 2 3 2 a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) 2 2 2 2 b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)
    30. 30. Example 4 Simplify. 3 2 3 2 a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) 3 2 3 2 6 x + 3x − 11x + 2x − 9 x − 5 x 2 2 2 2 b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)
    31. 31. Example 4 Simplify. 3 2 3 2 a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) 3 2 3 2 6 x + 3x − 11x + 2x − 9 x − 5 x 3 2 8 x − 6 x − 16 x 2 2 2 2 b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)
    32. 32. Example 4 Simplify. 3 2 3 2 a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) 3 2 3 2 6 x + 3x − 11x + 2x − 9 x − 5 x 3 2 8 x − 6 x − 16 x 2 2 2 2 b. ( x y − 2xy + 8) − (−7x y + 2xy − 4) 2 2 2 2 x y − 2xy + 8 + 7x y − 2xy + 4
    33. 33. Example 4 Simplify. 3 2 3 2 a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) 3 2 3 2 6 x + 3x − 11x + 2x − 9 x − 5 x 3 2 8 x − 6 x − 16 x 2 2 2 2 b. ( x y − 2xy + 8) − (−7x y + 2xy − 4) 2 2 2 2 x y − 2xy + 8 + 7x y − 2xy + 4 2 2 8 x y − 4 xy + 12
    34. 34. Example 4 Simplify. 2 2 2 2 2 c. ( x y + x − xy ) − (− y + y + xy + 4 x y )
    35. 35. Example 4 Simplify. 2 2 2 2 2 c. ( x y + x − xy ) − (− y + y + xy + 4 x y ) 2 2 2 2 2 x y + x − xy + y − y − xy − 4 x y
    36. 36. Example 4 Simplify. 2 2 2 2 2 c. ( x y + x − xy ) − (− y + y + xy + 4 x y ) 2 2 2 2 2 x y + x − xy + y − y − xy − 4 x y 2 2 2 −3x y + x − 2xy + y − y
    37. 37. Homework
    38. 38. Homework p. 378 #1-39 odd“Deeds, not stones, are the true monuments of the great.” - John L. Motley
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