Q. 164.3( 22 Votes )

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

Answer :

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.


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