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Question
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = 4x3 – 12x2 + 14x – 3, g(x) = 2x – 1
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Solution
Given, p(x) = 4x3 – 12x2 + 14x – 3 and g(x) = 2x – 1
Here, zero of g(x) is `1/2`.
When we divide p(x) by g(x) using remainder theorem, we get the remainder `p(1/2)`.
∴ `p(1/2) = 4(1/2)^3 - 12(1/2)^2 + 14(1/2) - 3`
= `4 xx 1/8 - 12 xx 1/4 + 14 xx 1/2 - 3`
= `1/2 - 3 + 7 - 3`
= `1/2 + 1`
= `(1 + 2)/2`
= `3/2`
Hence, remainder is `3/2`.
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