Add,sub,mult polynomials

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Add,sub,mult polynomials

  1. 1. 6.3 Adding, Subtracting, & Multiplying Polynomials p. 338
  2. 2. To + or - , + or – the coeff. of like terms! Vertical format : Add 3x3+2x2-x-7 and x3-10x2+8. 3x3 + 2x2 – x – 7 + x3 – 10x2 + 8 Line up like terms 4x3 – 8x2 – x + 1
  3. 3. Horizontal format : Combine like terms (8x3 – 3x2 – 2x + 9) – (2x3 + 6x2 – x + 1)= (8x3 – 2x3)+(-3x2 – 6x2)+(-2x + x) + (9 – 1)= 6x3 + -9x2 + -x + 8 = 6x3 – 9x2 – x + 8
  4. 4. Examples: Adding & Subtracting (9x3 – 2x + 1) + (5x2 + 12x -4) = 9x3 + 5x2 – 2x + 12x + 1 – 4 = 9x3 + 5x2 + 10x – 3 (2x2 + 3x) – (3x2 + x – 4)= 2x2 + 3x – 3x2 – x + 4 = 2x2 - 3x2 + 3x – x + 4 = -x2 + 2x + 4
  5. 5. Multiplying Polynomials: Vertically (-x2 + 2x + 4)(x – 3)= -x2 + 2x + 4 * x–3 3x2 – 6x – 12 -x3 + 2x2 + 4x -x3 + 5x2 – 2x – 12
  6. 6. Multiplying Polynomials : Horizontally (x – 3)(3x2 – 2x – 4)= (x – 3)(3x2) + (x – 3)(-2x) + (x – 3)(-4) = (3x3 – 9x2) + (-2x2 + 6x) + (-4x + 12) = 3x3 – 9x2 – 2x2 + 6x – 4x +12 = 3x3 – 11x2 + 2x + 12
  7. 7. Multiplying 3 Binomials : (x – 1)(x + 4)(x + 3) = FOIL the first two: (x2 – x +4x – 4)(x + 3) = (x2 + 3x – 4)(x + 3) = Then multiply the trinomial by the binomial (x2 + 3x – 4)(x) + (x2 + 3x – 4)(3) = (x3 + 3x2 – 4x) + (3x2 + 9x – 12) = x3 + 6x2 + 5x - 12
  8. 8. Some binomial products appear so much we need to recognize the patterns! Sum & Difference (S&D): (a + b)(a – b) = a2 – b2 Example: (x + 3)(x – 3) = x2 – 9 Square of Binomial: (a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 – 2ab + b2
  9. 9. Last Pattern Cube of a Binomial (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a – b)3 = a3 - 3a2b + 3ab2 – b3
  10. 10. Example: (x + 5)3 = a = x and b = 5 x3 + 3(x)2(5) + 3(x)(5)2 + (5)3 = x3 + 15x2 + 75x + 125

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