Question

If the polynomials ax³ + 4x² + 3x – 4 and x³ – 4x + a leave the same remainder when divided by (x – 3), the value of a is :

(a) 2 

(b) \(-\frac{3}{2}\)

(c) –1 

(d) 4

Answer 1

(c) -1

Let f(x) = ax³ + 4x² + 3x – 4 

g(x) = x³ – 4x + a. 

Remainders when f(x) and g(x) are divided by (x – 3) are f(3) and g(3) respectively. Now, 

f(3) = a. (3)³ + 4.(3)² + 3.3 – 4 

= 27a + 36 + 9 – 4 = 27a + 41                        ...(i) 

g(3) = (3)³ – 4.(3) + a = 27 – 12 + a = 15 + a            ...(ii) 

Given, f(3) = g(3)

∴ 27a + 41 = 15 + a ⇒ 26a = – 26 ⇒ a = – 1.