The remainder theorem of polynomials states: if a polynomial p(x) is divided by a binomial (x - a), the remainder obtained is p(a).
In this case, the polynomial is:
Applying the remainder theorem p(-2) = -18, that is:
Given that (x - 1) is a factor, then p(1) = 0, that is:
Now, we have a system of 2 equations and 2 variables: m and n. Subtracting equation 2 to equation 1, we get:
-8m + n = -46
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m + n = -1
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-9m = -45
m = (-45)/(-9)
m = 5
Substituting this result into equation 2, we get:
5 + n = -1
n = -1 - 5
n = -6