What is the complete square of q^2-4q+c

Question

Help me please! I need to know how to do the steps and get the right answer.

Answer 1

Don't let the letter "c" confuse you. All it means is that any number could go there, just as long as it fits the rest of the equation. In this case, you could factor the polynomial in two different way :

a. (q - 2)(q - 2)

or

b. (q - 3)(q - 1)

 

However, since you are looking for the "complete square", you know that the answer has to be choice "a" because the terms in parenthesis are both the same. In other words : 

(q - 2)(q - 2)  =  (q - 2)^2