Answer:
[tex](x-4)(x+9)[/tex]
Step-by-step explanation:
To factorize a quadratic equation, take into consideration that:
If [tex]ax^2+bx+c[/tex],
then [tex](x+w)(x+v)[/tex]
ONLY IF [tex]w+v=b[/tex] and [tex]wv=c[/tex].
To start, find factors of c, which in this case, -36:
1 and -36
2 and -18
3 and -12
4 and -9
6 and -6
-6 and 6
-4 and 9
-3 and 12
-2 and 18
-1 and 36
Try out which pair of numbers add up to b, which in this case, 5:
[tex]1+(-36)\neq 5\\2+(-18)\neq 5\\3+(-12)\neq 5\\4+(-9)\neq 5\\6+(-6)\neq 5\\-6+6\neq 5\\-4+9=5\\-3+12\neq 5\\-2+18\neq 5\\-1+36\neq 5[/tex]
The only pair of numbers that add up to 5 is -4 and 9, so:
[tex]x^2+5x-36\\=(x-4)(x+9)[/tex]
