When p(x) = x4 + 2x3 – 3x2 + x – 1 is divided by (x

Foundation

Mathematics Foundation

Remainder Theorem

Question

When p(x) = x⁴ + 2x³ – 3x² + x – 1 is divided by (x – 2), the remainder is

–15

–1

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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:

$p (2) = 2^{4} + 2 (2^{3}) - 3 (2^{2}) + 2 - 1$

$= 16 + 16 - 12 + 2 - 1$

$= 21$

Therefore, the remainder is 21.

Final Answer: 21