Foundation
Mathematics Foundation
Remainder Theorem
Question
When p(x) = x4 + 2x3 – 3x2 + x – 1 is divided by (x – 2), the remainder is
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Solution
To find the remainder when polynomial p(x) is divided by (x – 2), we use the Remainder Theorem. This theorem states that the remainder of this division is equal to p(2).
We substitute x = 2 into the polynomial:
p(2) = 24 + 2(23) − 3(22) + 2 − 1
= 16 + 16 − 12 + 2 − 1
= 21
Therefore, the remainder is 21.
Final Answer: 21