Synthetic Division of Polynomials

Learning Tool Last Enhanced on February 2, 2013 at 4:13 am by admin — 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.

x¹⁰+

x⁹+

x⁸+

x⁷+

x⁶+

x⁵+

x⁴+

x³+

x²+

x¹+

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:

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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