Synthetic Division of Polynomials

Learning Tool Last Enhanced on February 2, 2013 at 4:13 amadmin 8 Comments ↓

Use this automated synthetic division calculator to divide a polynomial (as high as 10th order) by a binomial and be able to quickly solve for the roots using this handy tool! Not only will it present a final answer, but it will walk you through each step of the synthetic division process, as well as provide a list of all possible rational roots to test.

*A javascript-enabled browser is required to use this tool.

Please select the order of the polynomial to be divided:

Then input the coefficients of each term. If a coefficient field is left blank, it is assumed to be ONE (1). Remember to include ZEROES (0) for missing terms and negative signs (-) where a minus appears in your equation. (Currently this only supports integers, fractions and decimals are not allowed). Once you supply the constant term at the end of the equation, a list of factors to determine possible rational roots will appear below.

Factors of p
Please Supply Coefficients Above
Factors of q
Please Supply Coefficients Above
Possible Rational Roots (p/q)
Please Supply Coefficients Above

*Remember, the factors and possible roots above can be negative (-) or positive (+).

Next, you'll need the binomial factor that you wish to divide by. For example, if dividing by or factoring out
x + 2, then the root or solution is -2 (when x + 2 = 0 is solved for x).
Please input the given root or solution to factor:

  • Pingback: Identify All Possible Rational Roots for a Polynomial with the Rational Root Theorem | The Crafty Canvas | Library of Academia()

  • chiara

    can anyone solve this for me? 2x^4 – 9x^3 + 6x – 3x + 48 divided by x-3

  • Dallin

    This is beautiful but you got p and q flipped (i.e., p is the constant factors; q is the leading coefficient)

  • fred bones

    an upper and lower bound attachment would be nice

  • alpha

    Yes, you got p and q flipped. P is supposed to be the constant. q is supposed to be the leading coefficient. A good way to remember this is that p has the loop pointed in this direction -> and q has it pointed this direction (p). And the leading coefficient is <- (q). qp. Horrible explanation but I hope someone gets it.

  • ted

    how do you make it negative sign

  • MeMeMe

    it wont give the factors of -24

  • jimboy001

    My teacher assignment to us give 60 example of synthetic division he said (px) (qx) (ox) (rx) plss help me can u give me just 20 30 40

  • oka

    i love oka