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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
Solution
p(x) = 4x3 – 12x2 + 14x – 3, g(x) = 2x – 1
Let g(x) = 2x – 1
2x – 1 = 0
2x = 1
∴ x = `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 + 7 - 3`
= `1/2 - 3 + 4`
= `(1 - 6 + 8)/2`
= `3/2`
∴ Remainder = `3/2`.
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