4x^2 - 20x + k
We want something like this :
(2x - √k) (2x - √k) = 4x^2 - 2√kx - 2√kx + k = 4x^2 - 4√kx + k
So....it appears that.we need to have
-20 = -4√k square both sides
400 = 16k divide both sides by 16
25 = k
Proof
(2x - √25) (2x - √25) =
(2x - 5)(2x - 5) =
(2x - 5)^2 =
4x^2 - 10x - 10x + 25 =
4x^2 - 20x + 25
So the binomial is just (2x - 5)