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Question
f(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
Solution
It is given that f(x) = 2x3 − 9x2 + x + 12 and g(x) = (3 − 2x)
By factor theorem, (3 − 2x) is the factor of f(x), if f(3/2)= 0
Therefore,
In order to prove that (3 − 2x) is a factor of f(x). It is sufficient to show that `f(3/2) = 0`
Now,
`f(3/2) = 2(3/2)^3 -9(3/2)^2 +(3/2) + 12`
` = 27/4 - 81/4 + 3/2 + 12`
` = 54 / 4 + 3/2 + 12`
` = -27/2 + 3/2 +12`
` = -12 + 12`
`= 0`
Hence, (3 − 2x), is the factor of polynomial f(x).
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