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Unità 6 - Polinomi

Exercise

81

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

xn−2xn+1−1x^n-2x^{n+1}-1xn−2xn+1−1, −3xn−xn+1+1-3x^n-x^{n+1}+1−3xn−xn+1+1

Solution

  • (xn−2xn+1−1)+(−3xn−xn+1+1)(x^n-2x^{n+1}-1)+(-3x^n-x^{n+1}+1)(xn−2xn+1−1)+(−3xn−xn+1+1) === xn−2xn+1−1−3xn−xn+1+1x^n-2x^{n+1}-1-3x^n-x^{n+1}+1xn−2xn+1−1−3xn−xn+1+1 === (xn−3xn)+(−2xn+1−xn+1)+(1−1)(x^n-3x^n)+(-2x^{n+1}-x^{n+1})+(1-1)(xn−3xn)+(−2xn+1−xn+1)+(1−1) === (−2xn)+(−3xn+1)+(0)(-2x^n)+(-3x^{n+1})+(0)(−2xn)+(−3xn+1)+(0) === −2xn−3xn+1-2x^n-3x^{n+1}−2xn−3xn+1
  • (xn−2xn+1−1)−(−3xn−xn+1+1)(x^n-2x^{n+1}-1)-(-3x^n-x^{n+1}+1)(xn−2xn+1−1)−(−3xn−xn+1+1) === xn−2xn+1−1+3xn+xn+1−1x^n-2x^{n+1}-1+3x^{n}+x^{n+1}-1xn−2xn+1−1+3xn+xn+1−1 === (xn+3xn)+(xn+1−2xn+1)+(−1−1)(x^n+3x^n)+(x^{n+1}-2x^{n+1})+(-1-1)(xn+3xn)+(xn+1−2xn+1)+(−1−1) === (4xn)+(−xn+1)+(−2)(4x^n)+(-x^{n+1})+(-2)(4xn)+(−xn+1)+(−2) === 4xn−xn+1−24x^n-x^{n+1}-24xn−xn+1−2

Altri Esercizi

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