Question

Find the remainder when p(x)=x⁴-3x³+2x²+x-1 is divided by x+2​

Answer 1

Answer:

By the remainder theorem,

(x-2)=0

x=2

p(x)=x^{4} -3x^{3} +2x^{2} +x+1

p(0)=16-24+8+2+1

=2

Hence the remainder is 2

Answer 2

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.