If Polynomials 2x3 + ax2 + 3x - 5 and x3 + x2 - 2x + a are divided by (x - 2), the same remainder are obtained. Find the value of a ________

f(x) = 2x3 + ax2 + 3x - 5

g(x) = x3 + x2 - 2x + a

By remainder theorem,

f(2) = 2(2)3 + a(2)2 + 3 × 2 - 5

= 17 + 4a

g(2) = (2)3 + (2)2 - 2 × 2 + a

= 8 + a

17 + 4a = 8 + a

3a = -9

a = -3