Answer:
The correct answer is 9.
Step-by-step explanation:
Using the Special Factoring Formula for Perfect square:
[tex]u^{2} - 2uv + v^{2} = (u - v)^{2}[/tex]
Since we have the given, [tex]x^{2} - 6x + __[/tex] ___,
We must think of a factor that adds up to -6x, and must lead to a perfect square.
A way to do this is by taking the coefficient middle term, -6, dividing it by 2, and squaring it:
[tex](\frac{6}{2})^{2} = (3)^{2} = 9[/tex]
Therefore, the missing constant term is 9.
To check whether it is correct, we can take [tex](x - 3)^{2}[/tex], and multiply using the FOIL method. We'll have the following answer:
[tex](x - 3) (x - 3)[/tex]
[tex]= x^{2} - 3x - 3x + 9[/tex]
[tex]= x^{2} - 6x + 9[/tex]
Therefore, we came up with the correct constant that completes the square, which is 9.
