How do you divide #(-2x^3-2x^2+7x+5)/(x-5) #?

To divide (-2x^3-2x^2+7x+5) by (x-5), you can use long division. Here are the steps:

1. Divide the first term of the numerator (-2x^3) by the first term of the denominator (x). The result is -2x^2.
2. Multiply the entire denominator (x-5) by -2x^2, giving -2x^3 + 10x^2.
3. Subtract this result from the original numerator: (-2x^3-2x^2+7x+5) - (-2x^3 + 10x^2) = -12x^2 + 7x + 5.
4. Bring down the next term from the numerator, which is 7x.
5. Divide the first term of the new numerator (-12x^2) by the first term of the denominator (x). The result is -12x.
6. Multiply the entire denominator (x-5) by -12x, giving -12x^2 + 60x.
7. Subtract this result from the new numerator: (-12x^2 + 7x + 5) - (-12x^2 + 60x) = -53x + 5.
8. Bring down the next term from the numerator, which is 5.
9. Divide the first term of the new numerator (-53x) by the first term of the denominator (x). The result is -53.
10. Multiply the entire denominator (x-5) by -53, giving -53x + 265.
11. Subtract this result from the new numerator: (-53x + 5) - (-53x + 265) = -260.
12. There are no more terms left in the numerator, so the division is complete.

The quotient is -2x^2 - 12x - 53, and the remainder is -260.