One Answer: 2/5
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Explanation:
Let's say that p is the leading coefficient and q is the last term.
To list out the possible rational roots, we need to find the factors of p and q. Dividing said factors over one another will lead to all the possible rational roots.
In this case, the leading coefficient is -5. The factors here are:
-1, 1, -5, 5
List the negative values as well as the positive values.
The factors of -2 are:
-1, 1, -2, 2
Now divide each factor of q = -2 over each factor of p = -5. It's very easy to get lost here because there are going to be 4*4 = 16 divisions going on. I recommend using a table to keep everything organized. See the chart below.
Anything in a gray box is a possible rational root. If we list the unique items only, we get this list = { -1, 1, -1/5, 1/5, -2/5, 2/5 } which are all the possible rational roots.
Compare those items with your possible answer choices. The only match here is 2/5
So 2/5 is the only possible answer in this case.
