How do you divide this polynomial using long division?

(6x^3-17x^2-104x-60) divide by (2x+5)

Here's a link for long division.

http://www.purplemath.com/modules/polydiv2.htm

Quite frequently we use synthetic division, with less writing to do:
http://www.purplemath.com/modules/synthdiv.htm

Hint: the given problem leaves no remainder.

To divide the polynomial (6x^3 - 17x^2 - 104x - 60) by (2x + 5) using long division, follow these steps:

Step 1: Arrange the polynomial and divisor in descending order of powers of x (from highest to lowest):
6x^3 - 17x^2 - 104x - 60
÷ (2x + 5)

Step 2: Divide the first term of the dividend (6x^3) by the first term of the divisor (2x).
(6x^3 ÷ 2x = 3x^2)

Step 3: Multiply the divisor (2x + 5) by the quotient obtained in the previous step (3x^2).
(3x^2 * (2x + 5) = 6x^3 + 15x^2)

Step 4: Subtract the result obtained in Step 3 from the dividend (6x^3 - 17x^2 - 104x - 60) - (6x^3 + 15x^2).
This can be done by changing the signs and combining like terms.
(-17x^2 - 104x - 60 - 15x^2) = (-32x^2 - 104x - 60)

Step 5: Bring down the next term from the dividend, which is -32x^2.
(-32x^2)

Step 6: Divide the new dividend (-32x^2 - 104x - 60) by the first term of the divisor (2x).
(-32x^2 ÷ 2x = -16x)

Step 7: Multiply the divisor (2x + 5) by the new quotient (-16x).
(-16x * (2x + 5) = -32x^2 - 80x)

Step 8: Subtract the result obtained in Step 7 from the new dividend (-32x^2 - 104x - 60) - (-32x^2 - 80x).
(- 32x^2 - 104x - 60 + 32x^2 + 80x) = (-24x - 60)

Step 9: Bring down the last term from the dividend, which is -24x.
(-24x)

Step 10: Divide the new dividend (-24x - 60) by the first term of the divisor (2x).
(-24x ÷ 2x = -12)

Step 11: Multiply the divisor (2x + 5) by the new quotient (-12).
(-12 * (2x + 5) = -24x - 60)

Step 12: Subtract the result obtained in Step 11 from the new dividend (-24x - 60) - (-24x - 60).
(-24x - 60 + 24x + 60) = 0

Step 13: Since there is no remainder, the final quotient is the sum of all the quotients obtained.
So, the polynomial (6x^3 - 17x^2 - 104x - 60) divided by (2x + 5) is equal to 3x^2 - 16x - 12.

Therefore, (6x^3 - 17x^2 - 104x - 60) ÷ (2x + 5) = 3x^2 - 16x - 12.