Question

If x power 5 -2x-kx-1 is divided by x+1 and the remainder is -1/2 find the value of k

Answer 1

Hello

(Note : x^5 means 'x to the power 5')

x^5 -2x - kx- 1 is divided by x+1 and the remainder is -1/2.

There is a simple logic.

Just add -1/2 to the equation so that the remainder becomes 0.(i.e. the equation becomes exactly divisible by x+1)

So x+1(x= -1) is a factor of the equation:-

》 x^5-2x-kx-1-1/2 = 0

》 x^5-2x-kx -3/2 = 0

Substitute x = -1

》 (-1)^5 -2(-1)-k(-1) -3/2 =0

》 -1+2+k-3/2 =0

》k = 3/2+1-2

》 k = 1/2

Hope it helps.

(Answer will help only if you understand it).