(6x²-7x-20)÷(2x-5)

Divide the first term of the numerator (6x²) by the first term of the denominator (2x). This gives you 3x. Multiply the entire denominator (2x - 5) by the quotient (3x): 3x * (2x - 5) = 6x² - 15x. Subtract this result from the numerator (6x² - 7x - 20): (6x² - 7x - 20) - (6x² - 15x) = -7x + 15x - 20 = 8x - 20. Now, you have 8x - 20 in the numerator. Repeat the process: Divide the first term of the new numerator (8x) by the first term of the denominator (2x). This gives you 4. Multiply the entire denominator (2x - 5) by the new quotient (4): 4 * (2x - 5) = 8x - 20. Subtract this result from the current numerator (8x - 20): (8x - 20) - (8x - 20) = 0. At this point, you have a remainder of 0, which means there are no more terms left in the numerator. Therefore, the result of the division is 3x + 4. So, (6x² - 7x - 20) ÷ (2x - 5) = 3x + 4.