Question

Using remainder theorem, find the remainder when p(x) = x³ + 3x² – 5x + 4 is divided by (x – 2).

Answer 1

Given: p(x) = x³ + 3x² – 5x + 4; divisor = (x – 2).

To Prove: Find the remainder when p(x) is divided by (x – 2).

Proof [Step-wise]:

1. Remainder Theorem: The remainder when a polynomial p(x) is divided by (x – a) equals p(a).

2. Apply the theorem with a = 2: remainder = p(2).

3. Compute p(2):

p(2) = 2³ + 3 × 2² – 5 × 2 + 4

= 8 + 12 – 10 + 4

= 14

The remainder when p(x) is divided by (x – 2) is 14.