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Unità 6 - Polinomi

Exercise

80

Determina la somma e la differenza dei polinomi delle seguenti coppie.

13x2−12x−2\dfrac{1}{3}x^2-\dfrac{1}{2}x-231​x2−21​x−2, −53x2+52x+4-\dfrac{5}{3}x^2+\dfrac{5}{2}x+4−35​x2+25​x+4

Solution

  • (13x2−12x−2)+(−53x2+52x+4)(\dfrac{1}{3}x^2-\dfrac{1}{2}x-2)+(-\dfrac{5}{3}x^2+\dfrac{5}{2}x+4)(31​x2−21​x−2)+(−35​x2+25​x+4) === 13x2−12x−2−53x2+52x+4\dfrac{1}{3}x^2-\dfrac{1}{2}x-2-\dfrac{5}{3}x^2+\dfrac{5}{2}x+431​x2−21​x−2−35​x2+25​x+4 === (13x2−53x2)+(52x−12x)+(4−2)(\dfrac{1}{3}x^2-\dfrac{5}{3}x^2)+(\dfrac{5}{2}x-\dfrac{1}{2}x)+(4-2)(31​x2−35​x2)+(25​x−21​x)+(4−2) === −43x2+42x+2-\dfrac{4}{3}x^2+\dfrac{\cancel{4}}{\cancel{2}}x+2−34​x2+2​4​​x+2 === −43x2+2x+2-\dfrac{4}{3}x^2+2x+2−34​x2+2x+2
  • (13x2−12x−2)−(−53x2+52x+4)(\dfrac{1}{3}x^2-\dfrac{1}{2}x-2)-(-\dfrac{5}{3}x^2+\dfrac{5}{2}x+4)(31​x2−21​x−2)−(−35​x2+25​x+4) === 13x2−12x−2+53x2−52x−4\dfrac{1}{3}x^2-\dfrac{1}{2}x-2+\dfrac{5}{3}x^2-\dfrac{5}{2}x-431​x2−21​x−2+35​x2−25​x−4 === (13x2+53x2)+(−12x−52x)+(−2−4)(\dfrac{1}{3}x^2+\dfrac{5}{3}x^2)+(-\dfrac{1}{2}x-\dfrac{5}{2}x)+(-2-4)(31​x2+35​x2)+(−21​x−25​x)+(−2−4) === 63x2+(−62x)+(−6)\dfrac{\cancel6}{\cancel3}x^2+(-\dfrac{\cancel6}{\cancel2}x)+(-6)3​6​​x2+(−2​6​​x)+(−6) === 2x2−3x−62x^2-3x-62x2−3x−6

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