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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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 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 × (− 2)2 + 4 × (− 2) + 32
= − 8 − 3 × 4 − 8 + 32 = − 8 − 12 − 8 + 32 = 4
Thus, the remainder is 4.
Final Answer: 4