State the possible rational roots of 2x^3-4x^2+8x-10=0

2x^{3} - 4x^{2} + 8x - 10 = 0

By the Rational Zeros Theorem, we can find all the possible rational zeros (or roots) of a polynomial function, such as this one, by the following:

Possible rational zeros **=** (factors of the constant term)
**/** (factors of the leading coefficient)

Make a list of all the possible factors of the constant term in the equation (which, in this case, is -10) and all the possible factors of the leading coefficient (which, in this case, is 2).

Factors of constant term, -10: ±1 , ±2 , ±5 , ±10

Factors of leading coefficient, 2: ±1 , ±2

Possible rational zeros **=** ±1, ±2, ±5, ±10 **/** ±1, ±2

**=** ±1**/**±1 , ±1**/**±2 , ±2**/**±1 , ±2**/**±2 , ±5**/**±1 , ±5**/**±2 , ±10**/**±1 , ±10**/**±2

**=** ±1 , ±1/2 , ±2 , ±1 , ±5 , ±5/2 , ±10 , ±5

**=** ±1 , ±2 , ±5 , ±10 , ±1/2 , ±5/2

Thus, you have the following 12 possible rational zeros/roots for this polynomial function:

** ± 1 , ± 2 , ± 5 , ± 10 , ± 1/2 , ± 5/2**