What is the Quotient of (15x^2 - 8x - 12) and (3x + 2)

To find the quotient of (15x² - 8x - 12) ÷ (3x + 2), we can follow the steps given below. These steps make the polynomial division process simple.

Step 1: Set up the division as a long division problem, with (15x² - 8x - 12) as the dividend and (3x + 2) as the divisor.

Step 2: Divide the leading term of the dividend (15x²) by the leading term of the divisor (3x), which gives 5x.

Step 3: Multiply the entire divisor (3x + 2) by this result (5x) to get (15x² + 10x).

Step 4: Subtract this result (15x² + 10x) from the dividend (15x² - 8x - 12) to get (-18x - 12).

Step 5: Divide the new leading term (-18x) by the leading term of the divisor (3x) to get -6.

Step 6: Multiply the entire divisor (3x + 2) by this result (-6) to get (-18x - 12).

Step 7: Subtract this from the previous remainder (-18x - 12) to get 0. The quotient is 5x - 6.

• Quotient: The result obtained after dividing one polynomial by another polynomial.

• Dividend: The polynomial being divided.

• Divisor: The polynomial by which the dividend is divided.

• Leading Term: The term in a polynomial with the highest degree.

• Remainder: The leftover part of the dividend that cannot be evenly divided by the divisor.