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Question
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
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Solution
Let the number to be subtracted from the given polynomial be k
Let f(x) = 16x3 – 8x2 + 4x + 7 – k
It is given that (2x + 1) is a factor of f(x).
∴ `f(-1/2) = 0`
`=> 16(-1/2)^3 - 8(-1/2)^2 + 4(-1/2)+7 - k = 0`
`=> -16 xx 1/8 - 8 xx 1/4 -4 xx 1/2 + 7 - k = 0`
`=>` –2 – 2 – 2 + 7 – k = 0
`=>` – 6 + 7 – K = 0
`=>` 1 – k = 0
`=>` k = 1
Thus, 1 should be subtracted from the given polynomial.
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