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

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

Mathematics
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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 \[\pm \frac{1}{5}\] \[\pm \frac{2}{5}\] \[\pm\frac{4}{5}\] \[\pm \frac{8}{5}\]
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.

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