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SLIDE SHOW INSTRUCTIONS This presentation is completely under your control.

SLIDE SHOW INSTRUCTIONS This presentation is completely under your control. This lesson will show only one step at a time, to see the next step you must press a key. (Actual names written on a key are in green ) TO STOP THE SLIDE SHOW : press ‘escape’ ( Esc , top left of keyboard)

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SLIDE SHOW INSTRUCTIONS This presentation is completely under your control.

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  1. SLIDE SHOW INSTRUCTIONS • This presentation is completely under your control. • This lesson will show only one step at a time, • to see the next step you must press a key. • (Actual names written on a key are in green) • TO STOPTHE SLIDE SHOW: press ‘escape’ (Esc, top left of keyboard) • TO MOVE FORWARD: press the “spacebar” or Enter • (PageDn,  , , also work) • TO MOVE BACKWARD: press the  key • (PageUp, or also work)

  2. Polynomial Addition: Like Terms

  3. x2 + 5x2 To add polynomials, we must CombineLike Terms Say we want to add these two polynomials: x2 - 3x + 4 and 5x2 - 2x - 2 Like Terms have exactly the same variables with exactly the same powers. These terms both have x2, so they are like terms 6x2 Combine Like Terms by adding or subtracting the coefficients, but keep the variables (and powers) the same. (Use the sign rules of integers to determine whether to add or subtract)

  4. -3x- 2x To add polynomials, we must CombineLike Terms Now add the next set of like terms: x2 - 3x + 4 and 5x2 - 2x - 2 Like Terms have exactly the same variables with exactly the same powers. These terms each have an x, so they are like terms 6x2 - 5x Combine Like Terms by adding or subtracting the coefficients, but keep the variables (and powers) the same. (Use the sign rules of integers to determine whether to add or subtract)

  5. +4- 2 To add polynomials, we must CombineLike Terms Now add the last set of like terms: x2 - 3x + 4 and 5x2 - 2x - 2 Like Terms have exactly the same variables with exactly the same powers. These terms are constants (numbers with no variables), so they are like terms 6x2 - 5x + 2 Answer: 6x2 - 5x + 2

  6. Horizontal Method

  7. Distribute the +1 One method of adding polynomials is called the Horizontal Method Add 2x2 - x - 7and -x2 + 3x - 4, use the Horizontal Method: Write the second polynomial in parentheses with a plus sign between them 2x2 - x - 7+ ( -x2 + 3x - 4) + 1 - x2 +3x - 4 2x2 - x - 7

  8. 2x2 - x2 x2 Horizontal Method: Polynomial Addition Now add the first set of like terms: 2x2 - x - 7 - x2 + 3x - 4 These terms both have x2, so they are like terms Combine Like Terms by adding or subtracting the coefficients, but keep the variables (and powers) the same. (Use the sign rules of integers to determine whether to add or subtract)

  9. -x+ 3x Horizontal Method: Polynomial Addition Now add the next set of like terms: 2x2 - x - 7 - x2 + 3x - 4 These terms each have an x, so they are like terms x2 + 2x

  10. -7- 4 Horizontal Method: Polynomial Addition Now add the next set of like terms: 2x2 - x - 7 - x2 + 3x - 4 These terms are constants (numbers with no variables), so they are like terms x2 + 2x - 11 Answer: x2 + 2x - 11

  11. Practice Problems: (Hit enter to see the answers) Add using the Horizontal Method 1) -6x2 + 2x + 1 and 3x2 - x + 2 5) 5x + 2x - 3 and 4x + 2 2) 5xy + 4x and -3xy - 12x 6) -3y2 + 2y and y2 + y - 1 3) 4ab + 2a2band 3ab 7) 2xy - 5x and - 3xy + 6x - 7 4) 3x2y +4x3y and - x3y + 2x2y 8) -17x + 6 and 3x - 6 Answers: 1) -3x2 + x + 3 2) 2xy - 8x 3) 2a2b + 7ab 4) 3x3y + 5x2y 5) 11x - 1 6) -2y2 + 3y - 1 7) -xy + x - 7 8) -14x

  12. Vertical Method

  13. Vertical Method: Polynomial Addition Add4x2 + 3x - 6 and 2x2 - 5x + 4,use the Vertical Method: 4x2 + 2x2 Write the two polynomials so that the like terms are stacked on top of each other These terms both have x2, so they are like terms

  14. Vertical Method: Polynomial Addition Add4x2 + 3x - 6 and 2x2 - 5x + 4,use the Vertical Method: 4x2 + 2x2 + 3x - 5x Write the two polynomials so that the like terms are stacked on top of each other These terms both have an x, so they are like terms

  15. Vertical Method: Polynomial Addition Add4x2 + 3x - 6 and 2x2 - 5x + 4,use the Vertical Method: 4x2 + 2x2 + 3x - 5x - 6 + 4 Write the two polynomials so that the like terms are stacked on top of each other These terms are constants, so they are like terms

  16. 4x2 + 2x2 + 3x - 5x - 6 + 4 Vertical Method: Polynomial Addition Add4x2 + 3x - 6 and 2x2 - 5x + 4,use the Vertical Method: Now draw a line under the whole thing and add the coefficients. 6x2 - 2x - 2 ANSWER =

  17. Vertical Method: Polynomial Addition Add x2 + 2 and 6x2 - 5x - 3, use the Vertical Method: x2 + 6x2 Write the two polynomials so that the like terms are stacked on top of each other These terms both have x2, so they are like terms

  18. + 0x - 5x (no x term?) Vertical Method: Polynomial Addition Add x2 + 2 and 6x2 - 5x - 3, use the Vertical Method: A problem that comes up when using the Vertical Method is that sometimes there are terms missing. x2 + 6x2 Solution: Write in a zero where there are missing terms. (Or you can leave a blank spot)

  19. Vertical Method: Polynomial Addition Add x2 + 2 and 6x2 - 5x - 3, use the Vertical Method: x2 + 6x2 + 0x - 5x + 2 - 3 Write the two polynomials so that the like terms are stacked on top of each other These terms are constants, so they are like terms

  20. x2 + 6x2 - 5x + 2 - 3 + 0x Vertical Method: Polynomial Addition Add x2 + 2 and 6x2 - 5x - 3, use the Vertical Method: Now draw a line under the whole thing and add the coefficients. 7x2 - 5x - 1 ANSWER =

  21. Suggestions for other situations: SituationSolution 1. A term has no coefficient showingWrite a “1” in front of it Example:x2 + 3x + 1 1x2 + 3x + 1 2. There are more than two like terms Stack (or group) all like terms together Ex: 2x + 6x - 3 and 4x + 5 (2x + 6x + 4x) + (-3 + 5) 3. There are many missing terms Write in zeros for each of them Ex: 5x3 - 2x and 4x4 + 3x2 + x - 6 0x4 + 5x3 + 0x2 - 2x + 0 4x4+ 0x3 + 3x2 + 1x - 6 4x4 + 5x3 + 3x2 + 1x - 6 4. Subtraction problem Distribute the (-1) before working the problem. x2 + 3x + 1 - (2x2 + 6x - 2)x2 + 3x + 1 - 2x2 - 6x + 2

  22. Practice Problems: (Hit enter to see the answers) Add using the Vertical Method 1)-6x2 + 2x + 1 and 3x2 - x + 2 5) 5x + 2x - 3 and 4x + 2 2) 5y + 4x and -3y - 12x 6) -3y2 + 2y and y2 + y - 1 3) 4ab + 2a2and 3ab 7) 2xy - 5x and - 3xy + 6x - 7 4) 3x2y +4xy and - xy + 2x2y 8) -17x2 + 6 and 3x - 6 Answers: 1) -3x2 + x + 3 2) 2y - 8x 3) 7ab + 2a2 4) 5x2y+ 3xy 5) 11x - 1 6) -2y2 + 3y - 1 7) -xy + x - 7 8) -17x2 + 3x

  23. End of Tutorial Go to www.greenebox.com for more great math tutorials for your home computer Questions? send e-mail to: lgreene1@satx.rr.com

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