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Question
What number should be added to polynomial f(x)= 12x3 + 16x2 - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?
Solution
(2x - 1) ⇒ x = `1/2`
When we substirute this value in the polynomial, whatever we get as a remainder (say a) should be added so that polynomial is exactly subtracted by the factor.
`"f"(1/2) = 12 xx (1/2) xx (1/2) xx (1/2) + 16 xx (1/2) xx (1/2) - 5 xx (1/2) - 8 + "a" = 0`
`=> 3/2 + 4 - 5/2 - 8 + "a" = 0`
⇒ a = 5
+ 4 - - 8 + a = Hence answer = 5
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