Answer: Choice B
[tex]\pm 8, \pm 4, \pm 2, \pm 1, \pm \frac{1}{2}[/tex]
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Explanation:
The first coefficient is 2. The last term is 8.
To find the possible rational roots, we look at factors of 2 and 8
factors of 2 = 1, 2
factors of 8 = 1,2,4,8
Then you divide each factor of 8 over the factor of 2. More generally, we divide the factors of the last term over the factors of the first coefficient.
A table is recommended so you can keep everything organized. See the diagram below.
The table shows 8, 4, 2, 1 and 1/2 as the unique results in each cell.
The table only shows the positive results, but the negative results will basically be identical except for the negative sign of course. The plus minus is to account for things like saying "-2 is a factor of 8 since -2*(-4) = 8". I find its easier to just focus on the positive and then stick plus minus at the end when all is said and done.
This is why choice B is the answer.
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Extra info:
Keep in mind this list is the possible rational roots and it does not mean they are all actual rational roots of the given polynomial. You'll need to plug each one into the polynomial to see if you get 0 as an output.
For instance, plugging x = 2 into y = 2x^2-10x+8 leads to y = -4 showing that x = 2 is not a root; however, x = 1 is a root because plugging x = 1 into y = 2x^2-10x+8 leads to y = 0. There's one other rational root for this polynomial.
