Int Math 2 Section 9-1
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Int Math 2 Section 9-1

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Add and Subtract Polynomials

Add and Subtract Polynomials

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Int Math 2 Section 9-1 Int Math 2 Section 9-1 Presentation Transcript

  • 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 see this: Part-time jobs, travel, geography, modeling
  • 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 variables without any addition or subtraction)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 variables without any addition or subtraction)2. Coefficient: The number that is with the variable3. Constant:4. Polynomial:5. Term:
  • 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:
  • 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:
  • 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
  • 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 polynomial is written from highest to lowest degree (highest to lowest exponent)9. Like Terms:
  • 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)
  • 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
  • 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
  • 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)
  • 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 )
  • 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 )
  • 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 )
  • 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 )
  • 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 )
  • 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
  • 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
  • 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 + 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 + 3y + 8 x − 2y − 4 x − y 5x
  • 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)
  • 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)
  • 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)
  • 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
  • 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
  • Example 4 Simplify. 2 2 2 2 2 c. ( x y + x − xy ) − (− y + y + xy + 4 x y )
  • 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
  • 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
  • Homework
  • Homework p. 378 #1-39 odd“Deeds, not stones, are the true monuments of the great.” - John L. Motley