What is the Quotient of (15x^2 - 8x - 12) and (3x + 2)
2026-02-21 21:09 Diff

106 Learners

Last updated on December 28, 2025

The result we get when we divide one polynomial by another polynomial is called the quotient. The quotient can be a polynomial itself, depending on the expressions involved. We will learn about the quotient of (15x^2 - 8x - 12) divided by (3x + 2) below.

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.

Explore Our Programs

Important Glossaries of Polynomial Quotient

  • 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.

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.