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Calculation Machine

Polynomial Long Division Calculator (Cubic ÷ Linear)

Divide a cubic by (x - r) with quotient and remainder.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Quotient
1x^2 + 1x + -2
Remainder
0
Divisor
(x - 3)
Check
(x-r) is a factor

Quick answer

Synthetic division by (x-r) gives a quadratic quotient and a constant remainder equal to P(r).

The formula

P(x) = (x-r)Q(x) + remainder

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • a (x^3 coeff)1
  • b (x^2 coeff)-2
  • c (x coeff)-5
  • d (constant)6
  • Divide by (x - r): r3

Result

  • Quotient1x^2 + 1x + -2
  • Remainder0
  • Divisor(x - 3)
  • Check(x-r) is a factor

How to use the Polynomial Long Division Calculator (Cubic ÷ Linear)

  1. 1Enter the coefficients of the cubic polynomial.
  2. 2Enter r, the root of the linear divisor (x - r).
  3. 3Read the quadratic quotient and the remainder from synthetic division.

Frequently asked questions

What if the remainder is zero?

It means (x-r) is an exact factor of the polynomial.

Does this work for higher degrees?

This tool is built for cubic ÷ linear; extend the same synthetic-division pattern for higher degrees.

About this calculator