Question

Divide the polynomials using long division: (2y^3 - 29y^2 + 90y) ÷ (y - 10).

Answer 1

To divide the polynomials using long division, divide each term in sequence, multiply the quotient by the divisor, and subtract from the numerator. Repeat the process until you can't divide further. The answer is the quotient plus any remainder over the divisor.

Step-by-step explanation:

To divide the polynomials (2y^3 - 29y^2 + 90y) ÷ (y - 10) using long division, follow these steps:

1. Divide the first term of the numerator, 2y^3, by the first term of the denominator, y, to get 2y^2, and write this above the division bar.
2. Multiply the entire divisor (y - 10) by this quotient, 2y^2, to get 2y^3 - 20y^2, and subtract this from the numerator.
3. Bring down the next term of the numerator, which will be -9y^2 (after the subtraction), and repeat the process using this new polynomial.
4. Divide -9y^2 by y to get -9y, multiply the divisor by -9y to get -9y^2 + 90y, subtract this from the polynomial you obtained in the last step, and bring down the next term, if there is any left.
5. Repeat the process until you have completed the division or the degree of the remainder is less than the degree of the divisor.

The result is the quotient, with a possible remainder, which can be expressed as a fraction over the original divisor.