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Question
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 6x2 + 2x – 4, g(x) = `1 - 3/2 x`
Solution
Given, p(x) = x3 – 6x2 + 2x – 4 and g(x) = `1 - 3/2 x`
Here, zero of g(x) is `2/3`.
When we divide p(x) by g(x) using remainder theorem, we get the remainder `p(2/3)`.
∵ `p(2/3) = (2/3)^3 - 6(2/3)^2 + 2(2/3) - 4`
= `8/27 - 6 xx 4/9 + 2 xx 2/3 - 4`
= `8/27 - 24/9 + 4/3 - 4`
= `(8 - 72 + 36 - 108)/27`
= `(-136)/27`
Hence, remainder is `(-136)/27`.
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