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Question
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
Solution 1
Let p(x) = x3 – ax2 + 6x – a
x - a = 0
∴ x = a
∴ Remainder = (a)3 - a(a)2 + 6(a) - a
= a3 - a3 + 6a - a
= 5a
Therefore, the remainder obtained is 5a.
Solution 2
By long division,
Therefore, when x3 − ax2 + 6x − a is divided by x − a, the remainder obtained is 5a.
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