The polynomials and when divided by (x-4) leave the same remainder. Find the value of a.

Let f(x) = ax³ + 3x² – 3

And,

g(x) = 2x³ - 5x + a

Now,

f(4) = a(4)³ + 3(4)² – 3

= 64a + 48 - 3

= 64a + 45

And,

g(4) = 2(4)³ – 5(4) + a

= 128 – 20 + a

= 108 + a

According to the question,

f(4) = g(4)

64a + 45 = 108 + a

64a – a = 108 – 45

63a = 63

a = 1

Hence, the value of ‘a’ is 1.