Polynomial Long Division Calculator
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Synthetic division is a method of performing polynomials long division. The method is used not for dividing out factors but for finding zero's (or roots) of polynomials. Ruffini's Rule is used for the long division. Here is an online algebra calculator for the synthetic division of polynomial equations using ruffini rule with a third degree. Enter decimal numbers in appropriate places for problem solving.

Ruffini Rule Calculator

x3+x2+x+
x+
 
Polynomial Result

Synthetic division is a method of performing polynomials long division. The method is used not for dividing out factors but for finding zero's (or roots) of polynomials. Ruffini's Rule is used for the long division. Here is an online algebra calculator for the synthetic division of polynomial equations using ruffini rule with a third degree. Enter decimal numbers in appropriate places for problem solving.

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Example

Solve a cubic equation 4x3+3x2+2x+7 by x+2.

From x+2, we can derive,
x = -2.
Let us consider the coefficients of the equation as : 4 3 2 7
Consider 0 as the quotient initially,
Hence the equation become as
      4     3     2     7
(-)   0
--------------------------------
     4
--------------------------------
Now multiply -2 with the remainder 4 (-2×4 = -8), which will be the quotient for the next step.

      4     3     2     7
(-)   0   -8
--------------------------------
      4   -5
--------------------------------

The next step is to multiply 5 with -2, to derive (5×-2 = -10), -10 should be used as the next quotient.
      4     3     2     7
(-)   0   -8     10
--------------------------------
      4   -5     12
--------------------------------

Multiply -8 with -2, to get 16.
      4     3     2     7
(-)   0   -8     10   -24
--------------------------------
      4   -5     12   -17
--------------------------------
Hence the polynomial equation is 4x²-5x+12 - 17/x+2.

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