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