Question 143850
Looking at {{{2x^2+5xy-2y^2}}} we can see that the first term is {{{2x^2}}} and the last term is {{{-2y^2}}} where the coefficients are 2 and -2 respectively.


Now multiply the first coefficient 2 and the last coefficient -2 to get -4. Now what two numbers multiply to -4 and add to the  middle coefficient 5? Let's list all of the factors of -4:




Factors of -4:

1,2,4


-1,-2,-4 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to -4

(1)*(-4)
-2*2
(-1)*(4)


note: remember, the product of a negative and a positive number is a negative number



Now which of these pairs add to 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th>
<tr><td align="center">1</td><td align="center">-4</td><td>1+(-4)=-3</td></tr>
<tr><td align="center">-2</td><td align="center">2</td><td>-2+(2)=0</td></tr>
<tr><td align="center">-1</td><td align="center">4</td><td>-1+4=3</td></tr>
</table>
None of these pairs of factors add to 5. So the expression {{{2x^2+5xy-2y^2}}} cannot be factored




Double check your book/worksheet to make sure that you have the correct problem.