Answer:
(x + 4)
Step-by-step explanation:
The given expression is
[tex]x^{2} -5x-36[/tex]
To its factor, we can use the quadratic formula
[tex]x_{1,2}=\frac{-b (+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Where
[tex]a=1\\b=-5\\c=-36[/tex]
Replacing these values in the quadratic formula, we have
[tex]x_{1,2}=\frac{-(-5) (+-)\sqrt{(-5)^{2}-4(1)(-36) } }{2(1)}=\frac{5(+-)\sqrt{25+144} }{2} =\frac{5(+-)\sqrt{169} }{2}=\frac{5(+-)13}{2}\\x_{1}=\frac{5+13}{2}=\frac{18}{2}=9\\x_{2}=\frac{5-13}{2}=\frac{-8}{2}=-4[/tex]
As you can observe the two factors must be [tex](x-9)(x+4)=0[/tex]
Therefore, the right answer is the second choice, (x + 4) is the other factor of the quadratic expression.
