Polynomial Long Division Calculator

Polynomial Long Division Calculator MathCelebrity logo Image to Crop Eevaluate the expression below:
2x7 + 3x6 - 6x5 + 6x4 - 2x3 - 8x2 + 6x - 1
x2 - 1

Setup long division format

Step 1
 1a)  Divide 2x7 ÷ x2
2x7 ÷ x2 = 2x(7 - 2) = 2x5

 1b) Multiply 1a by the divisor
2x5(x2 - 1) = 2x7 - 2x5
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 1c)  Subtract 2x7 - 2x5
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      2x5
x2 - 12x7 + 3x6 - 6x5 + 6x4 - 2x3 - 8x2 + 6x - 1
   2x7   - 2x5                  3x6 - 4x5 + 6x4 - 2x3 - 8x2 + 6x - 1   

Step 2
 2a)  Divide 3x6 ÷ x2
3x6 ÷ x2 = 3x(6 - 2) = 3x4

 2b) Multiply 2a by the divisor
3x4(x2 - 1) = 3x6 - 3x4
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 2c)  Subtract 3x6 - 3x4
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      2x5 + 3x4
x2 - 12x7 + 3x6 - 6x5 + 6x4 - 2x3 - 8x2 + 6x - 1
   2x7   - 2x5                  3x6 - 4x5 + 6x4 - 2x3 - 8x2 + 6x - 1        3x6   - 3x4                  -4x5 + 9x4 - 2x3 - 8x2 + 6x - 1   

Step 3
 3a)  Divide -4x5 ÷ x2
-4x5 ÷ x2 = -4x(5 - 2) = -4x3

 3b) Multiply 3a by the divisor
-4x3(x2 - 1) = -4x5 + 4x3
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 3c)  Subtract -4x5 + 4x3
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      2x5 + 3x4 - 4x3
x2 - 12x7 + 3x6 - 6x5 + 6x4 - 2x3 - 8x2 + 6x - 1
   2x7   - 2x5                  3x6 - 4x5 + 6x4 - 2x3 - 8x2 + 6x - 1        3x6   - 3x4                  -4x5 + 9x4 - 2x3 - 8x2 + 6x - 1          -4x5   + 4x3                  9x4 - 6x3 - 8x2 + 6x - 1   

Step 4
 4a)  Divide 9x4 ÷ x2
9x4 ÷ x2 = 9x(4 - 2) = 9x2

 4b) Multiply 4a by the divisor
9x2(x2 - 1) = 9x4 - 9x2
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 4c)  Subtract 9x4 - 9x2
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      2x5 + 3x4 - 4x3 + 9x2
x2 - 12x7 + 3x6 - 6x5 + 6x4 - 2x3 - 8x2 + 6x - 1
   2x7   - 2x5                  3x6 - 4x5 + 6x4 - 2x3 - 8x2 + 6x - 1        3x6   - 3x4                  -4x5 + 9x4 - 2x3 - 8x2 + 6x - 1          -4x5   + 4x3                  9x4 - 6x3 - 8x2 + 6x - 1            9x4   - 9x2                  -6x3 + x2 + 6x - 1   

Step 5
 5a)  Divide -6x3 ÷ x2
-6x3 ÷ x2 = -6x(3 - 2) = -6x

 5b) Multiply 5a by the divisor
-6x(x2 - 1) = -6x3 + 6x
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 5c)  Subtract -6x3 + 6x
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      2x5 + 3x4 - 4x3 + 9x2 - 6x
x2 - 12x7 + 3x6 - 6x5 + 6x4 - 2x3 - 8x2 + 6x - 1
   2x7   - 2x5                  3x6 - 4x5 + 6x4 - 2x3 - 8x2 + 6x - 1        3x6   - 3x4                  -4x5 + 9x4 - 2x3 - 8x2 + 6x - 1          -4x5   + 4x3                  9x4 - 6x3 - 8x2 + 6x - 1            9x4   - 9x2                  -6x3 + x2 + 6x - 1              -6x3   + 6x                  x2   - 1   

Step 6
 6a)  Divide x2 ÷ x2
x2 ÷ x2 = 1x(2 - 2) = 1

 6b) Multiply 6a by the divisor
1(x2 - 1) = x2 - 1
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 6c)  Subtract x2 - 1
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      2x5 + 3x4 - 4x3 + 9x2 - 6x + 1
x2 - 12x7 + 3x6 - 6x5 + 6x4 - 2x3 - 8x2 + 6x - 1
   2x7   - 2x5                  3x6 - 4x5 + 6x4 - 2x3 - 8x2 + 6x - 1        3x6   - 3x4                  -4x5 + 9x4 - 2x3 - 8x2 + 6x - 1          -4x5   + 4x3                  9x4 - 6x3 - 8x2 + 6x - 1            9x4   - 9x2                  -6x3 + x2 + 6x - 1              -6x3   + 6x                  x2   - 1                x2   - 1                        

We have no remainder:

2x5 + 3x4 - 4x3 + 9x2 - 6x + 1

You have 1 free calculations remaining

What is the Answer?

2x5 + 3x4 - 4x3 + 9x2 - 6x + 1

How does the Polynomial Long Division Calculator work?

Free Polynomial Long Division Calculator - Polynomial Long Division Calculator
This calculator has 2 inputs.

What 3 formulas are used for the Polynomial Long Division Calculator?

Divide the first term of the dividend by the first term of the divisor
We multiply that part of the quotient by the divisor
Subtract Step 2 from our main polynomial.

For more math formulas, check out our Formula Dossier

What 2 concepts are covered in the Polynomial Long Division Calculator?

divisionseparate a number into partspolynomial long divisionan algorithm for dividing a polynomial by another polynomial of the same or lower degree

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