Synthetic Division Calculator

Divide a cubic ax³ + bx² + cx + d by (x − r).

a (x³)

b (x²)

c (x)

d (constant)

Divisor root r

Quotient x² coeff 1

Quotient x coeff -5

Quotient constant 6

Remainder 0

Formula: Bring down, multiply by r, add — repeat

Step-by-step with your numbers:

1. Values used:

2. a (x³) = 1

3. b (x²) = -6

4. c (x) = 11

5. d (constant) = -6

6. Divisor root r = 1

8. Quotient x² coeff = 1

9. Quotient x coeff = a (x³) + b (x²) = 1 + -6 = -5

10. Quotient constant = 6

11. Remainder = 0

Did we solve your problem today?

Synthetic division is a fast shortcut for dividing a polynomial by a linear factor (x − r).

The math behind it

Bring down the leading coefficient, multiply by r and add to the next coefficient; repeat. The last number is the remainder, which by the Remainder Theorem equals f(r).

Worked example

(x³ − 6x² + 11x − 6) ÷ (x − 1) → quotient x² − 5x + 6, remainder 0.

FAQ

What does a zero remainder mean?

r is a root, so (x − r) is a factor of the polynomial.

The math behind it

Worked example

FAQ

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