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Question
f(x) = x5 + 3x4 − x3 − 3x2 + 5x + 15, g(x) = x + 3
Solution
It is given that f(x) = x5 + 3x4 − x3 − 3x2 + 5x + 15 and g(x) = x+3
By the factor theorem, g(x) is the factor of polynomial f(x).
i.e. x+3 =0
`f(-3) = (-3)^5 + 3(-3)^4 - (-3)^3 - 3(- 3)^2 + 5(-3) + 15`
f (−3) = 0
Hence, g(x) is the factor of polynomial f (x).
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