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Question
f(x) = x3 −6x2 − 19x + 84, g(x) = x − 7
Solution
It is given that f(x) = x3 −6x2 − 19x + 84, and g(x) = x − 7
By the factor theorem, g(x) is the factor of polynomial f(x), if f (7) = 0.
Therefore, in order to prove that (x − 7) is a factor of f(x).
It is sufficient to show that f(7) = 0
Now,
`f(7) = (7)^3 - 6(7)^2 - 19(7) + 84`
` = 343 - 294 - 133 + 84`
` = 427 - 427`
`=0`
Hence, (x − 7) is a factor of polynomial f(x).
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