This is one of the basic question from chapter 6 of factorisation from ML Aggarwal in which we have been asked to calculate the remainder (without division) on dividing f(x) by (x−2) where
f(x)=2x3−7x2+3
ML Aggarwal Avichal Publication
Factorisation Question no. 1(ii)
We know that the remainder theorem states that if a polynomial f(x) is divided by (x−a), the remainder is f(a).
(i) Here, we have the polynomial f(x)=5×2−7x+4 which is divided by (x−2), therefore, by remainder theorem, the remainder is:
R=f(2)=5(2)2 −7(2)+4
=(5×4)−14+4
=20−14+4
=24−14
=10
Hence, the remainder is 10.
(ii) Here, we have the polynomial f(x)=2×3−7×2 +3 which is divided by (x−2), therefore, by remainder theorem, the remainder is:
R=f(2)=2(2)3 −7(2)2 +3
=(2×8)−(7×4)+3
=16−28+3
=19−28
=−9
Hence, the remainder is −9.