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en.wikipedia.org/wiki/Synthetic_division

In algebra, synthetic division is a method of performing Euclidean division of polynomials, with less writing and fewer calculations than occur with polynomial ...

www.purplemath.com/modules/synthdiv.htm

Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor -- and it only works in this case.

Sal shows how synthetic division of polynomials works.

Let's do another synthetic division example. And in another video, we actually have the why this works relative to algebraic long division. But here it's going to be ...

www.mesacc.edu/~pikeu/mat120/notes/divide_poly/synthetic/synthetic_division.html

In order to divide polynomials using synthetic division, you must be dividing by a linear expression and the leading coefficient (first number) must be a 1.

www.emathhelp.net/calculators/algebra-1/synthetic-division-calculator

The calculator will divide the polynomial by the binomial using synthetic division, with steps shown.