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Unità 6 - Polinomi

Exercise

77

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

12x2+13x−1\dfrac{1}{2}x^2+\dfrac{1}{3}x-121​x2+31​x−1, −14x2+16x-\dfrac{1}{4}x^2+\dfrac{1}{6}x−41​x2+61​x

Solution

  • (12x2+13x−1)+(−14x2+16x)(\dfrac{1}{2}x^2+\dfrac{1}{3}x-1)+(-\dfrac{1}{4}x^2+\dfrac{1}{6}x)(21​x2+31​x−1)+(−41​x2+61​x) === 12x2+13x−1−14x2+16x\dfrac{1}{2}x^2+\dfrac{1}{3}x-1-\dfrac{1}{4}x^2+\dfrac{1}{6}x21​x2+31​x−1−41​x2+61​x === (12x2−14x2)(\dfrac{1}{2}x^2-\dfrac{1}{4}x^2)(21​x2−41​x2) +++ (13x+16x)(\dfrac{1}{3}x+\dfrac{1}{6}x)(31​x+61​x) +++ (−1)(-1)(−1) === 2−14x2+2+16x−1\dfrac{2-1}{4}x^2+\dfrac{2+1}{6}x-142−1​x2+62+1​x−1 === 14x2+36x−1\dfrac{1}{4}x^2+\dfrac{\cancel3}{\cancel6}x-141​x2+6​3​​x−1 === 14x2+12x−1\dfrac{1}{4}x^2+\dfrac{1}{2}x-141​x2+21​x−1
  • (12x2+13x−1)−(−14x2+16x)(\dfrac{1}{2}x^2+\dfrac{1}{3}x-1)-(-\dfrac{1}{4}x^2+\dfrac{1}{6}x)(21​x2+31​x−1)−(−41​x2+61​x) === 12x2+13x−1+14x2−16x\dfrac{1}{2}x^2+\dfrac{1}{3}x-1+\dfrac{1}{4}x^2-\dfrac{1}{6}x21​x2+31​x−1+41​x2−61​x === (12x2+14x2)+(13x−16x)+(−1)(\dfrac{1}{2}x^2+\dfrac{1}{4}x^2)+(\dfrac{1}{3}x-\dfrac{1}{6}x)+(-1)(21​x2+41​x2)+(31​x−61​x)+(−1) === 2+14x2+2−16x−1\dfrac{2+1}{4}x^2+\dfrac{2-1}{6}x-142+1​x2+62−1​x−1 === 34x2+16x−1\dfrac{3}{4}x^2+\dfrac{1}{6}x-143​x2+61​x−1

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