Question 83588
In order to factor {{{1*x^2+2*x+-15}}}, first we need to ask ourselves: What two numbers multiply to -15 and add to 2? Lets find out by listing all of the possible factors of -15


Factors:

1,3,5,15,

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

These factors pair up to multiply to -15.

(-1)*(15)=-15

(-3)*(5)=-15

 Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2

<TABLE><TR><TD>First Number</TD><TD>|</TD><TD>Second Number</TD><TD>|</TD><TD>Sum</TD></TR><TR><TD>1</TD><TD>|</TD><TD>-15</TD>|</TD><TD>|</TD><TD>1+(-15)=-14</TD></TR><TR><TD>3</TD><TD>|</TD><TD>-5</TD>|</TD><TD>|</TD><TD>3+(-5)=-2</TD></TR><TR><TD>-1</TD><TD>|</TD><TD>15</TD>|</TD><TD>|</TD><TD>(-1)+15=14</TD></TR><TR><TD>-3</TD><TD>|</TD><TD>5</TD>|</TD><TD>|</TD><TD>(-3)+5=2</TD></TR><TABLE>We can see from the table that -3 and 5 add to 2.So the two numbers that multiply to -15 and add to 2 are: -3 and 5


So m=-3, and n=5