Synthetic Division Calculator

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Synthetic Division of Polynomials

The division of polynonomial \( P(x) \) by the polynomial \( x - k \) may be written as follows
\( \dfrac{P(x)}{x - k)} = Q(x) + \dfrac{R}{x - k} \)
where \( Q(x) \) is the quotient and \( R \) is the remainder.
When the divisor is a linear polynomial of the form \( x - k\), the synthetic division may be used to divide a polynomial \(P(x) \) by the linear polynomial \( x - k \) and the remainder \( R \) is a constant.

Use of the Calculator

Enter all the coefficients, including the ones that are equal to zero, of the polynomial to divide (dividend) and entre \( k \) such that the divisor is \( x - k \). Press "Calculate" and check what you have entered before you accept the results given by the calculator.
NOTE: The coefficients are separated by commas with no comma at the start or the end. Also the coefficients whose values are equal to zero are entered as zeros.
For example the coefficients of the polynomial     \( -x^5+6x^4+4x^2+ 4 \)    are entered as       \( -1,6,0,4,0,4 \)

Enter Polynomial Coefficients:
k =
Decimal Places =


More references and links to polynomial functions

Synthetic Division of Polynomials with Examples
Applications of Synthetic Division of Polynomials
Factor Polynomials.
Polynomial Functions, Zeros, Factors and Intercepts