Question

Using remainder theorem, find the value of a if the division of x³ + 5x² – ax + 6 by (x – 1) leaves the remainder 2a.

Answer 1

Let x – 1 = 0, then x = 1
Substituting the value of x in f(x)
f(x) = x³ + 5x³ – ax + 6
= (1)³ + 5(1)² – a(1) + 6 
= 1 + 5 – a + 6
= 12 – a
∵ Remainder = 2a
∴ 12 – a = 2a
⇒ 12 = a + 2a
⇒ 3a – 12
∴ a = 4.