Given:
(x + 1)(x - 5) = -9
Let's select the correct statement from the given options.
Equate the equation to zero by adding 9 to both sides of the equation:
(x + 1)(x- 5) + 9 = -9 + 9
(x + 1)(x - 5) + 9 = 0
Expand the left side using FOIL method:
[tex]x(x-5)+1(x-5)+9=0[/tex]Apply distributive property:
[tex]x^2-5x+x-5+9=0[/tex]Combine like terms:
[tex]x^2-4x+4=0[/tex]Factor using the perfect square rule:
[tex]\begin{gathered} x^2-2\ast x\ast2+2^2=0 \\ \\ (x-2)^2=0 \end{gathered}[/tex]Thus, we have the factor:
[tex]x-2=0[/tex]Therefore, the correct statement is: x - 2 = 0
ANSWER:
x - 2 = 0