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Polynomial Operations Warm-Up: Addition and Subtraction Practice

This warm-up exercise involves collecting like terms and arranging them in descending order. It covers adding and subtracting polynomials, with detailed examples and practice problems included. Learn the rules for combining terms correctly to reinforce your understanding.

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Polynomial Operations Warm-Up: Addition and Subtraction Practice

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  1. 5 minutes Warm-Up Collect like terms and arrange in descending order. 1) 4x3 + 6x4 – 2x4 + 8x 2) 3x – 5x + 5 + 2x0 3) Evaluate 4x3 + x2 – 2 for x = 0 and x = 1

  2. Addition / Subtraction of Polynomials Objectives: To add polynomials To subtract polynomials

  3. Example 1 Add (5x2 + 3x + 4) + (3x2 + 5) = 8x2 + 3x + 9

  4. Example 2 Add (7x2y3 + xy) + (1 – 2x2y3) = 5x2y3 + xy + 1

  5. Practice Add. 1) (3x2 + 2x – 2) + (-2x2 + 5x + 5) 2) (31x4 + x2 + 2x – 1) + (-7x4 + 5x3 – 2x + 2) 3) (4a2b – 5a + 3) + (-2a2b – 2a – 4)

  6. Example 3 Add. (2x4 – 5x2 + 4x + 5) + (5x4 + 7x3 – 2x2 – 2x) 2x4 + 0x3 – 5x2 + 4x + 5 5x4 + 7x3 – 2x2 – 2x + 0 7x4 + 7x3 – 7x2 + 2x + 5

  7. Example 4 Add. (-3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1) + (5x5 – 3x3y3 – 5xy5) -3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1 5x5 - 3x3y3 - 5xy5 5x5 – 3x4y3 + 3x3y3 – 6x2 + 1

  8. Practice Add. 1) (-2m3 – 5m2 – 2m – 4) + (m4 – 6m2 + 7m – 10) 2) (-3x4y3 – 5xy + 2) + (x4y3 + x2 + 2xy + 5)

  9. Subtraction of Polynomials Objectives: To subtract polynomials

  10. Example 1 Subtract. (5x2 + 3x - 2) - (2x2 + 1) = 5x2 + 3x - 2 - 2x2 - 1 = 3x2 + 3x - 3

  11. Example 2 Subtract. (2x2y2 + 3xy3 – 4y4) - (x2y2 – 5xy3 + 3y – 2y4) = 2x2y2 + 3xy3 – 4y4 - x2y2 + 5xy3 – 3y + 2y4 = x2y2 + 8xy3 – 2y4 – 3y

  12. Practice Subtract. 1) (5x4 + 4) – (2x2 – 1) 2) (-7m3 + 2m + 4) – (-2m3 – 4) 3) (-3a2b4 + 5ab - 4) - (-4a3 + 11a2b4 – 2a - 6)

  13. Example 3 Subtract. (8x3 + 6x2 – 3x + 5) – (5x3 – 3x2 + 2x – 4) 8x3 + 6x2 – 3x + 5 -5x3 + 3x2 - 2x + 4 3x3 – 9x2 - 5x + 9

  14. Example 4 Subtract. (2a4b + 5a3b2 – 4a2b3) – (4a4b + 2a3b2 – 4ab) 2a4b + 5a3b2 – 4a2b3 -4a4b - 2a3b2 + 4ab -2a4b + 3a3b2 – 4a2b3 + 4ab

  15. Practice Subtract. 1) (-2m3 – 5m2 – 2m – 4) - (m4 – 6m2 + 7m – 10) 2) (-3x4y3 – 5xy + 2) - (x4y3 + x2 + 2xy + 5)

  16. RULE! • In order to add or subtract, you must have …. • The same BASE and the same EXPOENNT!

  17. Example • You can add 3x2 + 2x2 together • You CAN NOT add 3x3 + 2x2 together!

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