Learn the step-by-step process of dividing polynomials.
Division Algorithm
Given Dividend / Divisor:
Divide: Leading terms.
Multiply: Result by whole divisor.
Subtract: From the dividend.
Bring down: Next term and repeat.
Step-by-Step Example
Problem: (x² - 3x - 10) ÷ (x + 2)
Step 1: x² / x = x
Step 2: x(x + 2) = x² + 2x
Step 3: (x² - 3x) - (x² + 2x) = -5x
Step 4: -5x / x = -5
Step 5: -5(x + 2) = -5x - 10
Step 6: (-5x - 10) - (-5x - 10) = 0
Final Quotient: x - 5
About this calculator
What is Polynomial Long Division?
Polynomial long division is an algorithm for dividing one polynomial by another of the same or lower degree. It is very similar to the long division of numbers.
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Pro Tips
Divide the leading term of the dividend by the leading term of the divisor.
Multiply the divisor by the result and subtract from the dividend.
Repeat until the degree of the remainder is less than the degree of the divisor.
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Fun Facts
"If the remainder is zero, the divisor is a factor of the dividend."
"Synthetic division is a faster 'shortcut' method that works when the divisor is specifically in the form (x - a)."
