Question 87339
In order to factor {{{2*a^2+-4*a+-2}}}, first multiply 2 and -2 to get -4 and we need to ask ourselves: What two numbers multiply to -4 and add to -4? Lets find out by listing all of the possible factors of -4


Factors:

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 to multiply to -4.

(-1)*(4)=-4

(-2)*(2)=-4

 Now which of these pairs add to -4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -4

<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>-4</TD>|</TD><TD>|</TD><TD>1+(-4)=-3</TD></TR><TR><TD>2</TD><TD>|</TD><TD>-2</TD>|</TD><TD>|</TD><TD>2+(-2)=0</TD></TR><TR><TD>-1</TD><TD>|</TD><TD>4</TD>|</TD><TD>|</TD><TD>(-1)+4=3</TD></TR><TR><TD>-2</TD><TD>|</TD><TD>2</TD>|</TD><TD>|</TD><TD>(-2)+2=0</TD></TR><TABLE>

None of these factors add to -4. So the quadratic {{{2*a^2+-4*a+-2}}} cannot be factored.