Answer:
[tex](x-6)(x+1)[/tex]
Step-by-step explanation:
Factoring is usually just a bit of guess and check. [tex]x^2-5x-6[/tex] is written in the form [tex]a^2+b+c[/tex], where [tex]a=1[/tex], [tex]b=-5[/tex], and [tex]c=-6[/tex].
You need to find the two numbers that multiply together to equal [tex]-6[/tex] and can be added together to get [tex]-5[/tex]. These are [tex]-6[/tex] and [tex]1[/tex] in this case.
Now, put them together in the form [tex](x-6)(x+1)[/tex]. We will now check this answer using the FOIL method.
First term in each parentheses: [tex]x * x = x^2[/tex]
Outside terms: [tex]x * 1 = x[/tex]
Inside terms: [tex]-6 * x = -6x[/tex]
Last term in each parentheses: [tex]-6 * 1 = -6[/tex]
Now, add these together: [tex]x^2 + x - 6x - 6 = x^2 - 5x - 6[/tex]
Since we get the original expression, this is correct.
