Why should I use synthetic division instead of long division of polynomials?

Question

I know how to do synthetic division and long division. However, I don't really see why I should bother remembering synthetic division since it can't be utilized in all scenarios.

Hence my question is:

What type of problems require the usage of synthetic division to find an answer that long division would not allow me to find?

Answer 1

Snthetic division does away with the variables and focuses your attention on the coefficients. More efficient and takes up less space.

Synthetic divsion uses addition instead of subtraction. Less chance of error.

Synthetic division makes searching for rational roots much faster.

Syhthetic division is also the most efficient way to evaluate a polynomial at a given number.

Answer 2

No problem requires it, they give the same result (if done correctly), the synthetic division may just require less writing and be faster if you're skilled with it than the long division.

Answer 3

Everything you can do with synthetic division can be done with regular long division. The reverse is not true: you can’t find the quotient and remainder by synthetic division when dividing by a quadratic polynomial, for instance.