Find all possible rational zeros of U(x)=12x5+6x3−2x−8 using the rational zeros theorem (don't check to see which actually are zeros).
By the rational zeros theorem, the rational zeros of U are of the form
possible rational zero of U=factor of constant termfactor of leading coefficient=factor of 8factor of 12
The factors of 8 are ±1,±2,±4,±8 and the factors of 12 are ±1,±2,±3,±4,±6,±12. Thus, the possible rational zeros of U are
±11,±21,±41,±81,±12,±22,±42,±82,±13,±23,±43,±83,±14,±24,±44,±84,±16,±26,±46,±86,±112,±212,±412,±812.
Simplifying the fractions and eliminating duplicates, we get
±1,±2,±4,±8,±12,±13,±23,±43,±14,±16,±112.
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