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