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Answer :
Final answer:
The result of the division (35x⁸ - 45x³ + 20x²) by (5x²) is 7x⁶ - 9x.
Explanation:
To perform the division of the polynomial (35x⁸ - 45x³ + 20x²) by (5x²), we use polynomial long division. We start by dividing the highest-degree term of the numerator, which is 35x⁸, by the highest-degree term of the denominator, 5x². This results in 7x⁶ since 35x⁸ divided by 5x² is 7x⁶.
Now, we multiply the entire denominator, 5x², by 7x⁶ to get 35x⁸ and subtract it from the numerator. This leaves us with (-45x³ + 20x²).
Next, we repeat the process by dividing the highest-degree term of this new expression, -45x³, by 5x². This results in -9x since (-45x³) divided by (5x²) is -9x.
Again, we multiply the entire denominator, 5x², by -9x to get -45x³ and subtract it from the remaining expression, 20x². This leaves us with 20x² - (-45x³), which simplifies to 20x² + 45x³.
At this point, we have no terms left to divide, so our final answer is 7x⁶ - 9x.
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