Respuesta :

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.  

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