Question

Factorise x² + 5x - 36​

Answer 1

`(x-4)(x+9)`

Explanation:

To factorize a quadratic equation, take into consideration that:

If
`ax^2+bx+c`,

then
`(x+w)(x+v)`

ONLY IF
`w+v=b` and
`wv=c`.

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:

`1+(-36)\\eq 5\\2+(-18)\\eq 5\\3+(-12)\\eq 5\\4+(-9)\\eq 5\\6+(-6)\\eq 5\\-6+6\\eq 5\\-4+9=5\\-3+12\\eq 5\\-2+18\\eq 5\\-1+36\\eq 5`

The only pair of numbers that add up to 5 is -4 and 9, so:

`x^2+5x-36\\=(x-4)(x+9)`