f(x) = 4x^4 – 3x^3 – 2x^2 + x – 7, g(x) = x – 1

Question

Using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the by actual division :

f(x) = 4x⁴ – 3x³ – 2x² + x – 7, g(x) = x – 1

Answer 1

f(x) = 4x⁴ – 3x³ – 2x² + x – 7 

Put g(x) = 0

⇒ x – 1 = 0 or x = 1 

Remainder = f(1)

Now, 

f(1) = 4(1)⁴ – 3(1)³ – 2(1)² + (1) – 7 

= 4 – 3 – 2 + 1 – 7 

= -7

Actual Division: