Question

Divide: (2x^2 - 8xy + y^8) / (x - y). If there is a remainder, express it in the form of a fraction.

What is the result of the division (2x^2 - 8xy + y^8) / (x - y)?
a) 2x^2 - 10x - 10y + 9
b) 2x - 8y
c) 2x^2 - 10x - 9y + 9
d) 2x - 10y

Answer 1

The result of dividing the polynomial (2x^2 - 8xy + y^8) by (x - y) is 2x - 10y, which corresponds to option b). The polynomial division does not result in a remainder.

Step-by-step explanation:

We are tasked with dividing the polynomial (2x^2 - 8xy + y^8) by (x - y). Long division in algebra functions similarly to arithmetic long division, but we use coefficients and variables. Here's the step-by-step process of the division:

1. Divide the first term of the numerator by the first term of the denominator. So, 2x^2 divided by x is 2x. Write this above the division symbol.
2. Multiply the entire denominator by this quotient and subtract the product from the numerator.
3. Repeat these steps with the new polynomial that's left after the subtraction until the degree of the remainder is less than the degree of the denominator or until there is no remainder.

After applying these steps, the answer to the division problem is 2x - 10y, which corresponds to option b). There is no remainder in this case as the polynomial is perfectly divisible by the given denominator.