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# Polynomial Long Division

This calculator performs long division on two polynomials. It divides any polynomial by a polynomial of equal or lower degree. The calculator displays all steps on how the work was done.

Polynomial Long Division
input Dividend and divisor to get quotient and remainder
help ↓↓ examples ↓↓ tutorial ↓↓
(3x^2+3x-5)÷(x+2)
(2x^4-3x^2-x+2)÷(x^2+x-1)
 Divide the dividend by the divisor using long division Find the remainder when dividend is divided by the divisor Determine whether a divisor is a factor of the dividend

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Long division examples:
Question 1:ex 1:
Divide 3x^2 - 4x + 5 by x+2.
Question 2:ex 2:
What is the remainder when 4x^3-2x+11 is divided by x^2+1?
Question 3:ex 3:
Determine whether polynomial x-1 is a factor of x^5+2x^2-3x-4.
TUTORIAL

## How to calculate long division?

We can present long division algorithm with a simple example. Consider dividing the polynomial 3x2+4x-3 by x-3 using long division method. We can address this problem using a step-by-step approach.

Step 1: Identify the divisor and dividend and set up the division problem. In our example, the divisor is 3x2+4x-3, and the dividend is x-3. The division problem is:

_______________
x-3 | 3x^2+4x-3


Step 2:Divide the first term of a dividend 3x^2 by the first term of the divisor x.

      3x
_______________
x-3 | 3x^2+4x-3


Step 3:Multiply the divisor x-3 by the result from the last step (3x).

      3x
_______________
x-3 | 3x^2+4x-3
3x^2-9x


Step 4:Subtract

      3x
_______________
x-3 | 3x^2+4x-3
3x^2-9x
_________
13x-3


Step 5:Divide 13x by the first term of the divisor x.

      3x+13
_______________
x-3 | 3x^2+4x-3
3x^2-9x
_________
13x-3


Step 6:Multiply

      3x+13
_______________
x-3 | 3x^2+4x-3
3x^2-9x
_________
13x-3
13x-39


Step 7:Subtract

      3x+13
_______________
x-3 | 3x^2+4x-3
3x^2-9x
_________
13x-3
13x-39
-----
36


Solution: The quotient is 3x+13 and the remainder is 36.

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