Solving polynomial equations

[SureHeIS]

Which of the following represents the set of possible rational roots for the polynomial shown below?

2x³+5x²-8x-10=0

A {(1/2), 1, 2, (5/2), 4, 5, 10, 20}
B {+-1, +-2, +-4, +-5, +-10, +-20}
C {+-(1/2), +-1, +-2, +-(5/2), +-5, +-10}
D {+-(2/5), +-(1/2), +-1, +-2, +-(2/5), +-(1/5), +-(1/10)}

 

[SureHeIS]

Sorry, I ended up guessing (needed answer as soon as I could get it) the answer was C {+-(1/2), +-1, +-2, +-(5/2), +-5, +-10}

 

[MathLover1]

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is -10.

Find its factors (with the plus sign and the minus sign): ±1, ±2, ±5, ±10.

These are the possible values for p.

The leading coefficient (the coefficient of the term with the highest degree) is 2.

Find its factors (with the plus sign and the minus sign): ±1, ±2.

These are the possible values for q.

Find all possible values of p/q: ± 1/1 , ± 1/2, ±2/1,± 2/2, ± 5/1, ± 5/2, ± 10/1, ±10/2

Simplify and remove the duplicates (if any).

These are the possible rational roots: ±1,± 1/2 , ±2, ±5,± 5/2, ±10.