Question

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

Answer 1

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