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Enter the dividend and divisor to calculate the quotient and remainder of the polynomial division, with each step clearly shown.
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Our polynomial long division calculator allows you to divide any polynomial by another, providing the quotient, remainder, and a detailed, step-by-step explanation. Perfect for students, educators, and professionals, it simplifies algebraic divisions and ensures accurate results quickly. Use it to check homework, simplify rational expressions, or solve complex polynomial problems effortlessly!
Polynomial long division is a method in algebra used to divide one polynomial by another, breaking down complex expressions into simpler components for easier calculation and understanding.
This method is especially useful for:
Follow these standard steps to divide polynomials manually:
Write all polynomial terms in descending order of powers. Include missing terms with zero coefficients (Example: x³ + 2x + 1 → x³ + 0x² + 2x + 1).
Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient.
Multiply the divisor by the term obtained in Step 2 and subtract from the dividend to get the new remainder.
Bring down the next term from the dividend to form a new expression for the next division step.
Continue dividing, multiplying, and subtracting until the remainder's degree is lower than the divisor's degree.
Record the quotient and any leftover remainder.
Step 1: Divide the leading term:
2x³ ÷ x = 2x²
Step 2: Multiply and subtract:
2x²(x + 5) = 2x³ + 10x²
(2x³ - 3x² + 13x - 5) - (2x³ + 10x²) = -13x² + 13x - 5
Step 3: Repeat:
-13x² ÷ x = -13x
-13x(x + 5) = -13x² - 65x
(-13x² + 13x - 5) - (-13x² - 65x) = 78x - 5
Step 4: Final division:
78x ÷ x = 78
78(x + 5) = 78x + 390
(78x - 5) - (78x + 390) = -395
Final Answer:
2x³ - 3x² + 13x - 5 ÷ (x + 5) = 2x² - 13x + 78 + (-395 / (x + 5))
When to Use Long Division:
When to Use Synthetic Division:
If a polynomial f(x) is divided by x - c, the remainder is f(c). This allows quick remainder calculation without full division.
Yes, the quotient will be zero and the dividend itself becomes the remainder.
The division stops when the remainder’s degree is smaller than the divisor’s degree, ensuring a valid quotient and remainder.
Polynomial long division is systematic, reliable, and provides clear steps for accurate results.
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