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When $$x^4 + ax^3 + 5x^2 + 8x - 31$$ is divided by $$x - 2$$ the remainder is 5 then $$a$$ is
By the remainder theorem the remainder is $$f(2) = 16 + 8a + 20 + 16 - 31 = 21 + 8a$$. Setting $$21 + 8a = 5$$ gives $$a = -2$$.
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