We need to divide f(x) by (x-1/5) to find q(x) and r
f(x) = 20x³-34x²-1x+3
using synthetic division
1/5 | 20 -34 -1 3
_____ 4__-6_-7/5_
20 -30 -7 8/5
the numbers on the bottom represent the coefficients of the polynomial with each power of x reduced by one that is
our remainder = 8/5, so
r(x) = 8/5 or 1+3/5
and
q(x) = 20x^2 -30x -7
(This may be easier to see using long division)
and we end up with our original polynomial expressed as
f(x) = (x - 1/5)(20x^2 - 30x - 7) + 8/5
