Find the remainder when x³ – ax² + 6x – a is divided by x – a.

Concept Used:

Factor theorem: If (x – a) is a factor of f(x), then f(a) = 0

Explanation:

By long division method, we have

Therefore, the remainder obtained is 5a when x³ – ax² + 6x – a is divided by x – a
Remainder theorem:
Now to find the remainder when x³ – ax² + 6x – a is divided by x – a
we have to put x – a = 0, Thus x = a
Let f(x) = x³ – ax² + 6x – a
and f(a) will be the remainder
f(a) = a³ – a. a² + 6 a – a
f(a) = a³ – a³ + 5 a
f(a) = 5 a
Hence 5 a is the remainder when x³ – ax² + 6x – a is divided by x – a.