Question

Find the value of k if x – 2 is a factor of the polynomial Kx - 2x + k.

Answer 1

let k= x -2=0

x=2

put the value of x

now

kx-2x+k=0

k(2)-2(2)+k=0

k2-4+k=0

k=-4/2

k=-2

Answer 2

Given :-

(x - 2) is a factor of polynomial kx - 2x + k

➡ g(x) = x - 2 = 0

➡ x = 2

We know that,

When polynomials are divided by it's factors, remainder come 0.

By remainder theorem, we get

➡ p(2) = k(2) - 2(2) + k = 0

➡ 2k - 4 + k = 0

➡ 3k - 4 = 0

➡ 3k = 4

➡ k = 4/3

VERIFICATION :-

p(2) = 4/3(2) - 2(2) + 4/3

= 8/3 - 4 + 4/3

= 8/3 - 12/3 + 4/3

= -4/3 + 4/3

= 0/3

= 0

HENCE VERIFIED!

The value of k is = 4/3