Find the remainder (without division) on dividing 3x2+5x−9 by (3x+2).
I came across one of the basic question of factorisation but still finds it difficult to solve
Please give me a detailed solution of this question
Book- ML Aggarwal Avichal Publication, chapter 6, question no 4(ii)
Let us assume
3x+2=0
⇒x=−2/3
∴ By remainder theorem,
when f(x) is divided by (3x+2)
Remainder r=f(−2/3)
=3(−2/3)2+5(−2/3)−9
=4/3−10/3−9
=−6/3−9
=−2−9=−11
Hence, the remainder is −11