Question 21084
Factor:
{{{x^2 + 2x - 24}}} You are looking for two factors that look like this:
{{{(x + m)(x - n)}}} and when you multiply these two factors you will get the original expression back.
Now, what numbers goes in place of the m & n?
You want two integers whose product is -24 and whose sum is 2.
Here are some suggestions:
Try:
12 X (-2) = -24 ok
12 + (-2) = 10  No good!

Try: 
8 X (-3) = -24 ok
8 + (-3) = 5  No good!

Try:
6 X (-4) = -24 ok
6 + (-4) = 2 ok

The factors are: 
{{{(x + 6)(x - 4)}}}

Check:
{{{(x + 6)(x - 4) = x^2 -4x + 6x - 24}}} = {{{x^2 + 2x - 24}}}

The second problem is a little more difficult.

Factor: 
{{{2x^2 - 6xy - 8y^2}}} First factor a 2.
{{{2(x^2 - 3xy - 4y^2)}}} Now you want to find two factors that look like this:
{{{(x + my)(x - ny)}}}  What goes in place of the m & n? You want two integers whose product is -4 and whose sum is -3

Try: 
1 X (-4) = -4 Ok
1 + (-4) = -3 Ok

The complete factorisation is:
{{{2(x + y)(x - 4y)}}}

Check:
{{{2(x + y)(x - 4y) = 2(x^2 - 4xy + xy - 4y^2)}}} = {{{2(x^2 - 3xy - 4y^2) = 2x^2 - 6xy - 8y^2}}}