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Question
Prove by factor theorem that
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
Solution
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
3x - 2 = 0 ⇒ x = `2/3`
Substituting this value, we get
`"f" (2/3) = 18 xx (2/3) xx (2/3) xx (2/3) - 3 xx (2/3) xx (2/3) + 6 xx (2/3) - 8`
`= 16/3 - 4/3 + 4 - 8`
`= 4 + 4 - 8`
= 0
Hence (3x - 2) Is a factor of 18x3 - 3x2 + 6x -8.
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