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Question
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
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Solution
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
2x + 1 ⇒ x = `1/2`
Substituting this value, we get
`"f" (-1/2) = 4 xx (-1/2) xx (-1/2) xx (-1/2) + 12 xx (-1/2) xx (-1/2) xx (-1/2) + 7 xx (-1/2) + 1 = 0`
Hence (2x+ 1) 1s a factor of 4x3 + 12x2 + 7x + 1
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