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Question

Find the remainder when x3-ax2+6x-a is divisible by x-a.


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Solution

Find the remainder by using the remainder theorem:

Here, divident is x3-ax2+6x-9 and the divisor is x-a.

Let the polynomial px=x3-ax2+6x-a...(1)

Put Divisor=0.

x-a=0x=a

Theorem:

Remainder theorem states that when fx is divided by x-a, then the remainder is fa .

pa=a3-aa2+6a-a=a3-a3+6a-a=6a-a=5a

Hence, the remainder is 5a.


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