Question

if x-2 is a factor of (x-1)^5 - (2x + 5k)^2 then find value of k

Answer 1

Answer:

Using Factor theorem,

If x - 2 is a factor of the given polynomial, for x = 2, polynomial must be 0.

Therefore,

= > ( 2 - 1 )^5 - ( 2(2) + 5k )^2 = 0

= > (1)^5 - (4+5k)^2 = 0

= > 1 = (4+5k)²

= > 1 = 4 + 5k or - 1 = 4 + 5k

= > - 3 = 5k or - 5 = 5k

= > -3/5 = k or - 1 = k

Satisfying values of k are - 3/5 or - 1