7. What must be added to 2x⁴– 5x³ + 2x² – X-3 so
that the result is exactly divisible by (x – 2)?​

2 thoughts on “7. What must be added to 2x⁴– 5x³ + 2x² – X-3 so<br />that the result is exactly divisible by (x – 2)?​”

1. Answer:

   We will add the reminder which we will obtain when we divide 2x⁴ – 5x³ + 2x² – 8x

   – 3 by x – 2

   The remainder is 13

   Thus we will add -13

   For division

   = Refer to the attachment

   Thank you

   Reply

2. Let the required number to be added be k. Then ,

   p(x)=2x^4 =5x^3
   +2x^2
   −x−3+k

   and g(x)=(x−2).

   Now , g(x)=0

   x−2=0

   x=2.

   p(2)=0

   (32−40+8−5+k)=0

   k=5

   Reply