Question

The polynomials ax³ + 3x² – 3 and 2x³ − 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.

Answer 1

Let f (x) = ax³ + 3x² – 3

When f(x) is divided by (x − 4), remainder = f (4) 

f (4) = a (4)³ + 3(4)² − 3 = 64a + 45

Let g (x) = 2x³ − 5x + a

When g(x) is divided by (x − 4), remainder = g (4)

g (4) = 2(4)³ − 5(4) + a = a + 108

It is given that f (4) = g (4)

64a + 45 = a + 108

63a = 63

a = 1