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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.

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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

We can present long division algorithm with a simple example.
Consider dividing the polynomial 3x^{2}+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 3x^{2}+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.

RESOURCES

1. Synthetic division calculator

2. Long division calculator for integers

3. Tutorial on how to perform polynomial long division

4. Solved long division example — video tutorial.

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