Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

k² − 4k +

4.

Step-by-step explanation:

Hope this helps!

k² − 4k + 4

Step-by-step explanation:

recall the following property of perfect square quadratics

(a-b)² = a²- 2ab + b²  ( eq1)

We are given:

k² − 4k + ? (eq 2)

and we are asked to determine ? for which the expression above is a perfect square.

Manipulating the given equation:

k² − 4k + ?  (factor out 2 from the 2nd term), we get:

k² −(2)(k)(2) + ?

now we compare this with the right side of  (eq1)

a²- 2 a b + b²

we can clearly see that a = k and b = 2,

substituting this back into eq 2,

k² − 4k + 2²

= k² − 4k + 4