Question

List all possible rational solutions.
y=5x^(3)-2x^(2)+3x-8
Show work.
Thanks?

Answer 1

make a fraction. numerator must divide 8 so you have several possibilities :
1,2,4,8
denominator must divide 5 so only 2: 1,5
and of course they could be positive or negative. so you get a bunch of fractions that look like
so you get
\[\pm 1\]
\[\pm2\]
\[\pm4\]
\[\pm 8\]
those are the ones divided by 1 and you also get
\[\pm \frac{1}{5}\]
\[\pm \frac{2}{5}\]
\[\pm\frac{4}{5}\]
\[\pm \frac{8}{5}\]

Answer 2

btw i hope it is clear that the are POSSIBLE RATIONAL zeros. a cubic polynomial can have at most 3 zeros. and they need not all be rational.