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Question
What number should be subtracted from the polynomial f(x)= 2x3 - 5x2 +8x -17 so that the resulting polynomial is exactly divisible by (2x - 5)?
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Solution
(2x - 5) = 0 ⇒ x = `5/2`
When we substitute this value in the polynomial, whatever we get as a remainder (say a) should be subtracted so that polynomial is exactly subtracted by the factor.
`"f" (5/2) = 2 xx (5/2) xx (5/2) xx (5/2) - 5 xx (5/2) xx (5/2) + 8 xx (5/2) - 17 - "a" = 0`
`=> 125 /4 - 125/4 + 20 - 17 - "a" = 0`
⇒ a = 3
Hence answer = 3
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