Polynomial Long Division Calculator (Cubic ÷ Linear)
Divide a cubic by (x - r) with quotient and remainder.
Enter your values
Enter the a (x^3 coeff) you are working with.
Enter the b (x^2 coeff) you are working with.
Enter the c (x coeff) you are working with.
Enter the d (constant) you are working with.
Enter the divide by (x - r): r you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | Divide a cubic by (x - r) with quotient and remainder. |
|---|---|
| Category | Math |
| Inputs needed | a (x^3 coeff), b (x^2 coeff), c (x coeff), d (constant), Divide by (x - r): r |
| Main output | Quotient |
| Formula | P(x) = (x-r)Q(x) + remainder |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- a (x^3 coeff)
- Enter the a (x^3 coeff) you are working with.
- b (x^2 coeff)
- Enter the b (x^2 coeff) you are working with.
- c (x coeff)
- Enter the c (x coeff) you are working with.
- d (constant)
- Enter the d (constant) you are working with.
- Divide by (x - r): r
- Enter the divide by (x - r): r you are working with.
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.
What do I need to enter into the Polynomial Long Division Calculator (Cubic ÷ Linear)?
Just 5 values: a (x^3 coeff), b (x^2 coeff), c (x coeff), d (constant), divide by (x - r): r. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Polynomial Long Division Calculator (Cubic ÷ Linear) work out the answer?
Synthetic division by (x-r) gives a quadratic quotient and a constant remainder equal to P(r). It applies the formula P(x) = (x-r)Q(x) + remainder and shows the working so you can check each step by hand.
Is the Polynomial Long Division Calculator (Cubic ÷ Linear) free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.