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Question
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 4x2 + 5x + 3
Solution
Let 2x + 1 = 0, then x = `-(1)/(2)`
Substituting the value of x in f(x):
f(x) = 4x2 + 5x + 3
= `4(-1/2)^2 + 5 xx (-1/2) + 3`
= `4 xx (1)/(4) - (5)/(2) + 3`
= `1 - (5)/(2) + 3`
= `4 - (5)/(2)`
= `(3)/(2)`
∴ Remainder = `(3)/(2)`.
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