Polynomial Long Division Calculator (Cubic ÷ Linear)
Divide a cubic by (x - r) with quotient and remainder.
Enter 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).
P(x) = (x-r)Q(x) + remainder
How to use the Polynomial Long Division Calculator (Cubic ÷ Linear)
- 1Enter the coefficients of the cubic polynomial.
- 2Enter r, the root of the linear divisor (x - r).
- 3Read the quadratic quotient and the remainder from synthetic division.
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
Results
- Quotient1x^2 + 1x + -2
- Remainder0
- Divisor(x - 3)
- Check(x-r) is a factor
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
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.