−3/2 6138 3
###
####
Subsequent steps proceed as follows:
−3/2 6138 3
###
6###
−3/2 6138 3
− 9 ##
6###
−3/2 6138 3
− 9 ##
64##
−3/2 6138 3
− 9 − 6 #
64##
−3/2 6138 3
− 9 − 6 #
642#
−3/2 6138 3
− 9 − 6 − 3
642#
−3/2 6138 3
− 9 − 6 − 3
6420
We get a remainder of 0. This tells us that x=−3/2 is a real root of the original cubic equation. We can now
write it in binomial-trinomial form. The binomial factor is what we get when we subtract −3/2 from x.
Polynomial Equation of Third Degree 429