This is an important question from ML Aggarwal book, Avichal Publication in which we have been asked to find the remainder on dividing by 2x+1 of given polynomial
Factorisation chapter 6, question no 3(i)
Rajan@2021Guru
Find the remainder (without division) on dividing f(x) by (2x+1) where f(x)=4x 2 +5x+3
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Let us assume 2x+1=0
⇒2x=−1
⇒x=−1/2
By remainder theorem, when f(x) is divided by (2x+1)
Remainder r=f(−1/2)=4(−1/2)2+5(−1/2)+3
=4×1/4 −5/2 +3
=1– 5/2+3
=4-5/2
=(8-5)/2
=3/2
Hence the remainder is 3/2