(Use a version of the ac factoring method.)
3x^2 - xy - 24y^2
The product of the first and last coefficients is
3xx-24 = -72
We want to split the middle term -xy into two terms. The coefficient of this middle term is -1
So, we need two numbers whose product is -72 and whose sum is -1.
1xx-72 no, they do not add to -1
2xx-36 no
3xx-24 no
4xx-18 no
5xx no
6xx-12 no
7xx no
8xx-9 yes! the product is -72 and the sum is -1
Now split the middle term using 8xy and -9xy (In the end it won't matter which order you write them in, so let's just use the one above.)
3x^2 - xy - 24y^2
3x^2 +8xy - 9xy - 24y^2 Now factor by grouping.
(3x^2 +8xy)+( - 9xy - 24y^2)
= x(3x+8y)+(-3y)(3x+8y)
= (x-3y)(3x+8y)
Check by multiplying:
3x^2+8xy-9xy-24y^2 looks good, so we are finished.
