Question

Remainder theorem find remainder when x4 + x3 - 2x2 + x+1 is divided by x-1​

Answer 1

Required Answer:-

Question:

• Using remainder theorem, find the remainder when x⁴ + x³ - 2x² + x + 1 is divided by (x - 1)

Solution:

→ Let f(x) = x⁴ + x³ - 2x² + x + 1

Remainder theorem states that —

"If a polynomial f(x) is divided by (x - α), then remainder = f(α)"

So, if f(x) is divided by (x - 1), then,

→ Remainder = f(1) [As per remainder theorem]

So,

→ f(1) = (1)⁴ + (1)³ - 2 × (1)² + 1 + 1

→ f(1) = 1 + 1 - 2 + 1 + 1

→ f(1) = 4 - 2

→ f(1) = 2

→ Therefore, remainder obtained = 2.

Answer:

• Remainder = 2.