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Warm-up

7w. 3. Warm-up. State whether each expression is a polynomial. If the expession is a polynomial, identify it as either a monomial, binomial, or trinomial and give its degree. 1. 8a 2 + 5ab 2. 3x 2 + 4x – 7/x 3. 5x 2 + 7x + 2 4. 6a 2 b 2 + 7ab 5 – 6b 3 5. w 2 x - + 6x.

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Warm-up

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  1. 7w 3 Warm-up State whether each expression is a polynomial. If the expession is a polynomial, identify it as either a monomial, binomial, or trinomial and give its degree. 1. 8a2 + 5ab 2. 3x2 + 4x – 7/x 3. 5x2 + 7x + 2 4. 6a2b2 + 7ab5 – 6b3 5. w2 x - + 6x

  2. 7w 3 Warm-up State whether each expression is a polynomial. If the expession is a polynomial, identify it as either a monomial, binomial, or trinomial and give its degree. 1. 8a2 + 5ab binomial; 2 2. 3x2 + 4x – 7/x not a polynomial not the product of # and variable 3. 5x2 + 7x + 2 trinomial; 2 4. 6a2b2 + 7ab5 – 6b3 trinomial; 2 5. w2 x - + 6x trinomial; 2

  3. 2 3 4 1 4 4 4 8 Homework 6.5 9. 4 10. 5 11. 5 + 2x2 + 3x3 + x4 12. 1 + 3x + 2x2 13. - 6 + 5x + 3x2 14. 2 + x + 9x2 + x3 15. - 3 + 4x – x2 + 3x3 16. – 2x + x2 - x3 + x4

  4. Homework 6.5 17. 6 + 12x + 6x2 + x3 18. 21r2 + 7r5x – r2x2 – 15x3 19. 5x3 - 3x2 + x+ 4 20. - x3 + x2 - x+ 1 21. 3x3 + x2 - x+ 27 22. 3x3 + x2 + x - 17 23. x3 + x - 1 24. 3x3 + x2 - x+ 64

  5. Homework 6.5 25. - x3 + x + 25 26. ⅓px3 + p3 x2 + px+ 5p

  6. 6.6 Adding and Subtracting Polynomials CORD Math Mrs. Spitz Fall 2006

  7. Objectives: • After studying this lesson, you should be able to add and subtract polynomials.

  8. Assignment: • 6.6 Worksheet

  9. The standard measurement for a window is the united inch. The united inch measurement of a window is equal to the sum of the length of the length and the width of the window. If the length of the window at the right is 2x + 8 and the width is x – 3 inches, what is the size of the window in united inches? Application: x – 3 in. 2x + 8 in.

  10. The size of the window is (2x + 8) + (x – 3) inches. To add two polynomials, add the like terms. = (2x +8) + (x - 3) = 2x + 8 + x – 3 = (2x + x) + (8 – 3) = 3x + 5 The size of the window in united inches is 3x + 5 inches. Application: x – 3 in. 2x + 8 in.

  11. Application • You can add polynomials by grouping the like terms together and then finding the sum (as in the example previous), or by writing them in column form.

  12. Example 1: Find (3y2 + 5y – 6) + (7y2 -9) Method 1: Group the like terms together. (3y2 + 5y – 6) + (7y2 -9) = (3y2 + 7y2) + 5y + [-6 + (-9)] = (3 + 7)y2 + 5y + (-15) = 10y2 + 5y - 15

  13. Example 2: Find (3y2 + 5y – 6) + (7y2 -9) Method 2: Column form Recall that you can subtract a rational number by adding its additive inverse or opposite. Similarly, you can subtract a polynomial by adding its additive inverse.

  14. To find the additive inverse of a polynomial, replace each term with its additive inverse. The additive inverse of every term must be found!!!

  15. Example 2: Find (4x2 – 3y2 + 5xy) – (8xy+ 6x2 + 3y2) Method 1: Group the like terms together. (4x2 – 3y2 + 5xy) – (8xy+ 6x2 + 3y2) = (4x2 – 3y2 + 5xy) + (– 8xy - 6x2 - 3y2) = (4x2 - 6x2) + (5xy – 8xy) + (- 3y2 - 3y2) = (4 - 6)x2 + (5 – 8)xy + (-3 - 3)y2 = -2x2 – 3xy + -6y2 OR WOULD YOU PREFER COLUMN FORMAT?

  16. Example 2: Find (4x2 – 3y2 + 5xy) – (8xy+ 6x2 + 3y2) Column format First, reorder the terms so that the powers of x are in descending order: (4x2 + 5xy – 3y2) – (6x2 + 8xy+ 3y2) THEN use the additive inverse to change the signs

  17. Example 2: Find (4x2 – 3y2 + 5xy) – (8xy+ 6x2 + 3y2) Column format To check this result, add -2x2 – 3xy + -6y2 and 6x2 + 8xy+ 3y2 (4x2 + 5xy – 3y2) This is what you should get after you check it.

  18. The perimeter is the sum of the measures of the three sides of the triangle. Let s represent the measure of the third side. Example 3: Find the measure of the third side of the triangle. P is the measure of the perimeter. 3x2 + 2x - 1 s 8x2 – 8x + 5 P = 12x2 – 7x + 9

  19. (12x2 – 7x + 9) = (3x2 + 2x - 1) + (8x2 – 8x + 5) + s (12x2 – 7x + 9) - (3x2 + 2x - 1) - (8x2 – 8x + 5) = s 12x2 – 7x + 9 - 3x2 - 2x + 1 - 8x2 + 8x - 5) = s (12x2 - 3x2 - 8x2)+(– 7x - 2x + 8x) + (9 + 1 - 5) = s x2 - x + 5 = s The measure of the third side is x2 - x + 5.

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