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Question
f(x) = 3x3 + x2 − 20x +12, g(x) = 3x − 2
Solution
It is given that `f(x) = 3x^3 + x^3 - 20x + 12` and g(x) = 3x − 2
By the factor theorem,
(3x − 2) is the factor of f(x), if `f(2/3) =0`
Therefore,
In order to prove that (3x − 2) is a factor of f(x).
It is sufficient to show that `f(2/3) =0.`
Now,
`f(2/3) = 3(2/3)^3 + (2/3) ^2 - 20(2/3) +12`
`= 3(8/27) + 4/9 - 40/3 + 12`
` = 8/9 + 4/9 - 40 /3 + 12`
` = 12/9 - 4/3`
` = 4/3 - 4/3`
`= 0`
Hence, (3x − 2) is the factor of polynomial f(x).
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