When p(x) = x3 – 3x2 + 4x + 32 is divided by (x + 2), the remainder is

Foundation

Mathematics Foundation

Remainder Theorem

Question

When p(x) = x³ – 3x² + 4x + 32 is divided by (x + 2), the remainder is

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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 p(x) ÷ (x - a) is equal to p(a).

Here, the divisor is (x + 2), which can be written as (x - (-2)). Therefore, a = -2. We substitute x = -2 into p(x):

$p (- 2) = {(- 2)}^{3} - 3 \times {(- 2)}^{2} + 4 \times (- 2) + 32$

$= - 8 - 3 \times 4 - 8 + 32 = - 8 - 12 - 8 + 32 = 4$

Thus, the remainder is 4.

Final Answer: 4