Math

Polynomial Division Calculator

Divide ax² + bx + c by a linear divisor dx + e.

a (x²)

b (x)

c (constant)

Divisor d (x)

Divisor e (constant)

Calculated Output

Quotient x coeff 1

Quotient constant 3

Remainder 0

Formula: Long division of polynomials

Step-by-Step Breakdown

1. Values used:

2. a (x²) = 1

3. b (x) = 5

4. c (constant) = 6

5. Divisor d (x) = 1

6. Divisor e (constant) = 2

8. Quotient x coeff = 1

9. Quotient constant = 3

10. Remainder = 0

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The math behind it

Polynomial long division works like numeric long division: divide the leading terms, multiply back, subtract, and repeat with the remainder.

(x² + 5x + 6) ÷ (x + 2) = x + 3, remainder 0.

When is synthetic division better?

Synthetic division is quicker but only works when dividing by a monic linear factor (x − r).