Question

. Divide the polynomial x4 +2x3
-2x2
-x+1 by x+1 by long division and verify the remainder by
using remainder theorem.

Answer 1

Step-by-step explanation:

x4 +2x3

-2x2x4 +2x3

-2x2

Answer 2

QUESTION:-

Divide the polynomial x⁴ +2x³ -2x²-x+1 by x+1 by long division and verify the remainder by  using remainder theorem.

EXPLANATION:-

1) USING REMAINDER THEOREM

[KINDLY GO THROUGH THE ATTACHMENT]

2)Verifying by remainder theorem

Let p(x)= x⁴ +2x³ -2x²-x+1

and g(x)=x+1

x+1=0

x=-1

So remainder =p(-1)

p(-1)= (-1)⁴ +2(-1)³ -2(-1)²-(-1)+1

p(-1)=1-2-2+1+1

p(-1)=-3+1+1

p(-1)=-1

So remainder=p(-1)=-1

Since the remainder obtained by polynomial long divison and that by remainder theorem is equal .SO verified