document.write( "Question 129969: how to factor quadratic equation: 5X^2 + 25X + 5= 0 \n" ); document.write( "

Algebra.Com's Answer #94923 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

$\"5%2Ax%5E2%2B25%2Ax%2B5\"$ Start with the given expression.

$\"5%28x%5E2%2B5x%2B1%29\"$ Factor out the GCF $\"5\"$ .

Now let's try to factor the inner expression $\"x%5E2%2B5x%2B1\"$

---------------------------------------------------------------

Looking at the expression $\"x%5E2%2B5x%2B1\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"5\"$ , and the last term is $\"1\"$ .

Now multiply the first coefficient $\"1\"$ by the last term $\"1\"$ to get $\"%281%29%281%29=1\"$ .

Now the question is: what two whole numbers multiply to $\"1\"$ (the previous product) and add to the second coefficient $\"5\"$ ?

To find these two numbers, we need to list all of the factors of $\"1\"$ (the previous product).

Factors of $\"1\"$ :

1

-1

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to $\"1\"$ .

1*1 = 1
(-1)*(-1) = 1

Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"5\"$ :

\n" ); document.write( "

First Number	Second Number	Sum
1	1	1+1=2
-1	-1	-1+(-1)=-2

From the table, we can see that there are no pairs of numbers which add to $\"5\"$ . So $\"x%5E2%2B5x%2B1\"$ cannot be factored.

===============================================================

Answer:

So $\"5%2Ax%5E2%2B25%2Ax%2B5\"$ simply factors to $\"5%28x%5E2%2B5x%2B1%29\"$

In other words, $\"5%2Ax%5E2%2B25%2Ax%2B5=5%28x%5E2%2B5x%2B1%29\"$ .

\n" ); document.write( " \n" ); document.write( "

\n" );