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Question
Prove by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
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Solution
(2x - 1) is a factor of 6x3 - x2 - 5x +2
2x -1 = 0 ⇒ x = `1/2`
Substituting this value, we get
`"f" (1/2) = 6 xx 1/2 xx 1/2 xx 1/2 - 1/2 xx 1/2 - 5 xx 1/2 + 2`
`= 3/4 - 1/4 - 5/2 + 2`
`= 1/2 - 5/2 + 2 = - 2 + 2 = 0`
Hence (2x - 1) is a factor of 6x3 - x2 - 5x +2
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