Question

What is the remainder obtained when p(x) = x⁴ + x³ + 2x² - x + 1 is divided by x + 1?
1. 5
2. 4
3. 3
4. 2

Answer 1

Correct Answer - Option 2 : 4

Given:

p(x) = x4 + x3 + 2x2 - x + 1

Divisor = x + 1

Calculation:

p(x) = x4 + x3 + 2x2 - x + 1      ----(1)

By using remainder theorem,

⇒ x + 1 = 0

⇒ x = -1

From equation (1)

p(x) = (-1)⁴ + (-1)³ + 2 × (-1)² - (-1) + 1

⇒ p(x) = 1 -1 + 2 + 1 + 1

⇒ P(x) = 4

∴ The remainder is 4.