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Question
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
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Solution
p(x) = 4x3 - 3x2 + 2x - 4 ...(i)
By the remainder theorem the required remainder
= p`(-1/2)`.
Put x = `(-1/2)` in equation (i) we get
`p(-1/2) = 4(-1/2)^3 -3 (-1/2)^2 + 2(-1/2)-4`
= `4 xx (1/8) -3 xx (1)/(4) + 2 xx (-1/2)-4`
= `-(1)/(2) - (3)/(4) -1 -4`
= `(-2 -3 -4 -16)/(4)`
= `-(25)/(4)`
Hence, the remainder is `-(25)/(4)`.
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