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Ad ding and subtracting Polynomials

Ad ding and subtracting Polynomials. TOPIC IX: Quadratic Equations and Functions. Lesson 8-1. POLYNOMIALS. What does each prefix mean?. mono one bi two tri three. Monomial.

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Ad ding and subtracting Polynomials

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  1. Adding and subtracting Polynomials TOPICIX:Quadratic Equations and Functions Lesson 8-1

  2. POLYNOMIALS

  3. What does each prefix mean? mono one bi two tri three

  4. Monomial Monomial is a real number, a variable, or a product of a real number and one or more variables with whole-number exponent. Here are some examples of monomials

  5. What about poly? polynomial one or more A polynomial is a monomial or a sum/difference of monomials. Important Note!! An expression is not a polynomial if there is a variable in the denominator.

  6. You can name a polynomial based on its degree or the number of monomials it contains

  7. State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x3yz2 monomial 3) not a polynomial

  8. Which polynomial is represented by X 1 X 1 X2 X • x2 + x + 1 • x2 + x + 2 • x2 + 2x + 2 • x2 + 3x + 2 • I’ve got no idea!

  9. Degree of a polynomial The degree of a monomial is the sum of the exponents of the variables.Find the degree of each monomial. 1) 5x22 • 4a4b3c 8 • -3 0

  10. To find the degree of a polynomial, find the largest degree of the terms. 1) 8x2 - 2x + 7 Degrees: 2 1 0 Which is biggest? 2) y7 + 6y4 + 3x4m4 Degrees: 7 4 8 2 is the degree! 8 is the degree!

  11. Find the degree of x5 – x3y2 + 4 • 0 • 2 • 3 • 5 • 10

  12. A polynomial is normally put in ascending or descending order. What is ascending order? Going from small to big exponents. What is descending order? Going from big to small exponents.

  13. Standard form of a Polynomial Means that the degrees of its monomial term decrease from left to right

  14. Put in descending order: • 8x - 3x2 + x4 - 4 x4 - 3x2 + 8x - 4 2) Put in descending order in terms of x: 12x2y3 - 6x3y2 + 3y - 2x -6x3y2 + 12x2y3 - 2x + 3y

  15. 3) Put in ascending order in terms of y: 12x2y3 - 6x3y2 + 3y - 2x -2x + 3y - 6x3y2 + 12x2y3 • Put in ascending order: 5a3 - 3 + 2a - a2 -3 + 2a - a2 + 5a3

  16. Write in ascending order in terms of y:x4 – x3y2 + 4xy–2x2y3 • x4 + 4xy– x3y2–2x2y3 • –2x2y3 – x3y2 + 4xy + x4 • x4 – x3y2–2x2y3 + 4xy • 4xy –2x2y3 – x3y2 + x4

  17. Adding and Subtracting Polynomials

  18. You can add and subtract monomial by adding and subtracting like terms. Examples: • = • =

  19. A polynomial is a monomial or a sum of monomial. The following polynomial is the sum of the monomial , Degree of each monomial

  20. ADDING Polynomial You can add polynomials by adding like terms What is the simpler form of 12) Method 1 – Add vertically Line up like terms then add the coefficients 12 8 Method 2 – Add horizontally Group like terms then add the coefficients 12) = 812

  21. Subtracting Polynomial Recall that subtraction means to add the opposite. So when you subtract a polynomial, change each of the term to its opposite. Then add the coefficients What is the simpler form of 12) Method 1 – Subtract vertically Line up like terms 12 Then add the opposite of each term in the polynomial being subtracted 12

  22. Subtracting Polynomial What is the simpler form of 12) Method 2 – Subtract horizontally ( ) Write the opposite of each term in the polynomial being subtracted = = ( Group like term = Simplify

  23. 1. Add the following polynomials:(9y - 7x + 15a) + (-3y + 8x - 8a) Examples: Group your like terms. (9y - 3y) + (- 7x + 8x) + (15a - 8a) = 6y + x + 7a

  24. 2. Add the following polynomials:(3a2 + 3ab - b2) + (4ab + 6b2) Combine your like terms. (3a2) + (3ab + 4ab) + (6b2 - b2) 3a2 + 7ab + 5b2

  25. Add the polynomials.+ Y X X2 Y X XY Y X Y 1 1 Y Y 1 1 1 1 1 1 Y • x2 + 3x + 7y + xy + 8 • x2 + 4y + 2x + 3 • 3x + 7y + 8 • x2 + 11xy + 8

  26. 3. Add the following polynomials using column form (vertically):(4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2) Line up your like terms. 4x2 - 2xy + 3y2 + -3x2 - xy + 2y2 _________________________ x2 - 3xy + 5y2

  27. 4. Subtract the following polynomials:(9y - 7x + 15a) - (-3y + 8x - 8a) Rewrite subtraction as adding the opposite. 9y - 7x + 15a +3y - 8x + 8a Group the like terms. 9y + 3y -7x - 8x + 8a +15a 12y - 15x + 23a

  28. 5. Subtract the following polynomials:(7a - 10b) - (3a + 4b) Rewrite subtraction as adding the opposite. (7a - 10b) + (-3a - 4b) Group the like terms. 7a - 3a - 10b - 4b 4a - 14b

  29. 6. Subtract the following polynomials using column form:(4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2) Line up your like terms and add the opposite 4x2 - 2xy + 3y2 +(+ 3x2+xy- 2y2) 7x2 - xy + y2

  30. Find the sum or difference.(5a – 3b) + (2a + 6b) • 3a – 9b • 3a + 3b • 7a + 3b • 7a – 3b

  31. Find the sum or difference.(5a – 3b) – (2a + 6b) • 3a – 9b • 3a + 3b • 7a + 3b • 7a – 9b

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