SOLUTION: Factor the following polynomial completely. 20x2 + 22xy + 6y2 =

Question 307198: Factor the following polynomial completely.
20x2 + 22xy + 6y2 =
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression

Factor out the GCF

Now let's focus on the inner expression

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Looking at we can see that the first term is and the last term is where the coefficients are 10 and 3 respectively.

Now multiply the first coefficient 10 and the last coefficient 3 to get 30. Now what two numbers multiply to 30 and add to the middle coefficient 11? 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 11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 11

First Number	Second Number	Sum
1	30	1+30=31
2	15	2+15=17
3	10	3+10=13
5	6	5+6=11
-1	-30	-1+(-30)=-31
-2	-15	-2+(-15)=-17
-3	-10	-3+(-10)=-13
-5	-6	-5+(-6)=-11

From this list we can see that 5 and 6 add up to 11 and multiply to 30

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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So our expression goes from and factors further to

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Answer:

So factors to

In other words,
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