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Objective: The learner will..,

9.1 Adding and Subtracting Polynomials. Objective: The learner will..,. NCSCOS. Write polynomials in standard form, Add and Subtract polynomials, by combining or subtracting like terms. 1.01. 9.1 Adding and Subtracting Polynomials. Identify each polynomial by the name and degree. 12.

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Objective: The learner will..,

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  1. 9.1 Adding and Subtracting Polynomials Objective: The learner will.., NCSCOS • Write polynomials in standard form, • Add and Subtract polynomials, by combining or subtracting like terms • 1.01

  2. 9.1 Adding and Subtracting Polynomials Identify each polynomial by the name and degree 12 monomial constant 8x – 5 binomial linear 4x + 3 binomial linear x2 + 6 binomial quadratic 3x2 + 6x + 5 trinomial quadratic x3 + 2x – 2 trinomial cubic x3 + 4 binomial cubic

  3. 9.1 Adding and Subtracting Polynomials Standard form: the terms of the polynomial are in descending order, meaning, the greatest exponent to the smallest (left to right). 2x2 + 7 x3 + 6x2 6x2 + x3 -4x2 + x + 9 9 + x – 4x2 a + a2 + a3 + 1 a3 + a2 + a + 1 8 – 3m2 – m3 + 2m – m3 – 3m2 + 2m + 8

  4. 9.1 Adding and Subtracting Polynomials Adding Polynomials in horizontal form: (x2 + 2x + 5) + (3x2 + x + 12) = 4x2 + 3x + 17 in vertical form: x2 + 2x + 5 + 3x2 + x + 12 = 4x2 + 3x + 17

  5. 9.1 Adding and Subtracting Polynomials 3x2 – 4x + 8 x2 + x + 1 Simplify: + 2x2 – 7x – 5 + 2x2 + 3x + 2 5x2 – 11x + 3 3x2 + 4x + 3 (4b2 + 2b + 1) + (7b2 + b – 3) a2 + 8a – 5 + 3a2 + 2a – 7 11b2 + 3b – 2 4a2 + 10a – 12

  6. 9.1 Adding and Subtracting Polynomials 7d2 + 7d z2 + 5z + 4 Simplify: + 2d2 + 3d + 2z2 - 5 9d2 + 10d 3z2 + 5z – 1 (2x2 – 3x + 5) + (4x2 + 7x – 2) (a2 + 6a – 4) + (8a2 – 8a) 9a2 – 2a – 4 6x2 + 4x + 3

  7. 9.1 Adding and Subtracting Polynomials 3d2 + 5d – 1 7p2 + 5 Simplify: + (–4d2– 5d + 2) + (–5p2– 2p + 3) –d2 + 1 2p2– 2p + 8 (3x2 + 5x) + (4 – 6x – 2x2) (x3 + x2 + 7) + (2x2 + 3x – 8) x2– x + 4 x3 + 3x2 + 3x – 1

  8. 9.1 Adding and Subtracting Polynomials Simplify: 4p2 + 5p 2x3 + x2 – 4 + (-2p + p + 7) + 3x2 – 9x + 7 4p2 + 4p + 7 2x3 + 4x2 – 9x + 3 5y2 – 3y + 8 + 4y3 – 9 (8cd – 3d + 4c) + (-6 + 2cd – 4d) 4y3 + 5y2 – 3y – 1 4c – 7d + 10cd – 6

  9. 9.1 Adding and Subtracting Polynomials Simplify: (12y3 + y2 – 8y + 3) + (6y3 – 13y + 5) (7y3 + 2y2 – 5y + 9) + (y3 – y2 + y – 6) (6x5 + 3x3 – 7x – 8) + (4x4 – 2x2 + 9) = 18y3 + y2 – 21y + 8 = 8y3 + y2 – 4y + 3 = 6x5 + 4x4 + 3x3 – 2x2 – 7x + 1

  10. 9.1 Adding and Subtracting Polynomials Subtracting Polynomials (Note: subtraction is adding the opposite) (5x2 + 10x + 2) – (x2 – 3x + 12) (5x2 + 10x + 2) + (–x2) + (3x) + (–12) = 4x2 + 13x – 10 5x2 + 10x + 2 = 5x2 + 10x + 2 –(x2 – 3x + 12) = –x2 + 3x – 12 4x2 + 13x – 10

  11. 9.1 Adding and Subtracting Polynomials Simplify: (3x2 – 2x + 8) – (x2 – 4) 3x2 – 2x + 8 + (–x2) + 4 = 2x2 – 2x + 12 (10z2 + 6z + 5) – (z2 – 8z + 7) 10z2 + 6z + 5 + (–z2) + 8z + (–7) = 9z2 + 14z – 2

  12. 9.1 Adding and Subtracting Polynomials Simplify: 3x2 – 7x + 5 7a2 – 2a – (x2 + 4x + 7) – (5a2+ 3a) 2x2 – 11x – 2 2a2 – 5a 7x2 – x + 3 4x2 + 3x + 2 – (3x2 – x – 7) – (2x2 – 3x – 7) 2x2 + 6x + 9 4x2 + 10

  13. 9.1 Adding and Subtracting Polynomials Simplify: 2x2 + 5x 3x2 – 2x + 10 – (x2 – 3) – (2x2+ 4x – 6) x2 – 6x + 16 x2 + 5x + 3 4x2 – x + 6 3x2 – 5x + 3 – (3x2 – 4) – (2x2 – x – 4) x2 – 4x + 7 x2 – x + 10

  14. 9.1 Adding and Subtracting Polynomials Simplify: (4x5+ 3x3 – 3x – 5) – (–2x3 + 3x2 + x + 5) = 4x5 + 5x3 – 3x2 – 4x – 10 (4d4– 2d2 + 2d + 8) – (5d3 + 7d2 – 3d – 9) = 4d4 – 5d3 – 9d2 + 5d + 17 (a2+ ab– 3b2) – (b2 + 4a2 – ab) = –3a2 + 2ab – 4b2

  15. 9.1 Adding and Subtracting Polynomials Simplify by finding the perimeter: x2 + x c2 + 1 6c + 3 A B 2x2 2x2 4c2+ 2c + 5 x2 + x A = 5c2 + 8c + 9 B = 6x2 + 2x

  16. 9.1 Adding and Subtracting Polynomials Simplify by finding the perimeter: 2d2 + d – 4 3x2 – 5 x D C 3d2– 5d x2 + 7 3d2– 5d d2 + 7 D = 9d2 – 9d + 3 C = 8x2 – 10x + 14

  17. 9.1 Adding and Subtracting Polynomials Simplify by finding the perimeter: 3x2– 5x a3 + 2a a + 1 E F x2 + 3 2a3+ a + 3 E = 3a3 + 4a + 4 F = 8x2– 10x + 6

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