Foundation
Mathematics Foundation
Remainder Theorem
Question
When p(x) = x3 – ax2 + x is divided by (x – a), the remainder is
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Solution
To find the remainder when polynomial p(x) is divided by (x – a), we use the Remainder Theorem. The theorem states that the remainder is equal to p(a).
First, substitute x = a into the polynomial p(x):
p(a) = a3 − a × a2 + a = a3 − a3 + a = a
Therefore, the remainder is simply a.
Final Answer: a