Question 133696
Let's see if we can factor {{{-2x^2-7x-15}}}





Looking at {{{-2x^2-7x-15}}} we can see that the first term is {{{-2x^2}}} and the last term is {{{-15}}} where the coefficients are -2 and -15 respectively.


Now multiply the first coefficient -2 and the last coefficient -15 to get 30. Now what two numbers multiply to 30 and add to the  middle coefficient -7? Let's list all of the factors of 30:




Factors of 30:

1,2,3,5,6,10,15,30


-1,-2,-3,-5,-6,-10,-15,-30 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to 30

1*30

2*15

3*10

5*6

(-1)*(-30)

(-2)*(-15)

(-3)*(-10)

(-5)*(-6)


note: remember two negative numbers multiplied together make a positive number



Now which of these pairs add to -7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -7


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">30</td><td>1+30=31</td></tr><tr><td align="center">2</td><td align="center">15</td><td>2+15=17</td></tr><tr><td align="center">3</td><td align="center">10</td><td>3+10=13</td></tr><tr><td align="center">5</td><td align="center">6</td><td>5+6=11</td></tr><tr><td align="center">-1</td><td align="center">-30</td><td>-1+(-30)=-31</td></tr><tr><td align="center">-2</td><td align="center">-15</td><td>-2+(-15)=-17</td></tr><tr><td align="center">-3</td><td align="center">-10</td><td>-3+(-10)=-13</td></tr><tr><td align="center">-5</td><td align="center">-6</td><td>-5+(-6)=-11</td></tr></table>

None of these pairs of factors add to -7. So the expression {{{-2x^2-7x-15}}} cannot be factored




So make sure that you copied the problem down correctly