Question

find the remainder when x⁴-3x³+2x²+2x+1 is divided by x-1​

Answer 1

Let,

P(x) = x⁴- 3x³ + 2x² + 2x + 1

   

So,

g(x) =  x - 1

⇒ x = 1

 

To be found :

The remainder when g(x) is divided by P(x)

P(1) = (1)⁴- 3(1)³ + 2(1)² + 2(1) + 1  

 [ ∵ as 1*1*1*1 = 1, 1*1*1 = 3, 1*1 = 2 ]

      = 1 - 3(1) + 2(1) + 2 + 1

      = 1 - 3 + 2 + 2 + 1

      = 1 + 2 + 2 + 1 - 3

      = 6 - 3

      = 3  

 

Hence,

The remainder is 3.