I just learned synthetic division of polynomials and was wondering what allows it to work? Why does it work?N An example of a problem would be $(4b^3+27b^2-15b-52)/(b+7)$ You write the -7 in the corner, line up the coefficients Drop down the first # Multiply it by the -7 add it to the second number and repeat:
- -15. -52
-28. 7. 56
- -1. -8. 4
Therefore the quotient would be $4b^2-b-8+(4/b+7)$ Why does this work?