Question

What must be added to the polynomial x 4 - 2x ​3 - 2x 2 + x - 1 so that the resulting polynomial is exactly divisible by x 2 - 2x - 3.

Answer 1

x2 - 2x - 3  has  x  + 1  as  one  factor. hence  if  we  put x = -1

value  of  polynomial  should  be  zero  by  remainder  therom

substituting  x = -1,  we get  value of  P( x ) = -1

Answer : 1  should  be  added