SOLUTION: What do I solve this by factoring? 20x^2 + 13x + 2 Thanks!

Question 139519: What do I solve this by factoring?
20x^2 + 13x + 2
Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 20 and 2 respectively.

Now multiply the first coefficient 20 and the last coefficient 2 to get 40. Now what two numbers multiply to 40 and add to the middle coefficient 13? Let's list all of the factors of 40:

Factors of 40:
1,2,4,5,8,10,20,40

-1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 40
1*40
2*20
4*10
5*8
(-1)*(-40)
(-2)*(-20)
(-4)*(-10)
(-5)*(-8)

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

Now which of these pairs add to 13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 13

First Number	Second Number	Sum
1	40	1+40=41
2	20	2+20=22
4	10	4+10=14
5	8	5+8=13
-1	-40	-1+(-40)=-41
-2	-20	-2+(-20)=-22
-4	-10	-4+(-10)=-14
-5	-8	-5+(-8)=-13

From this list we can see that 5 and 8 add up to 13 and multiply to 40

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 )

Set the factorization equal to zero

Now set each factor equal to zero:
or

or Now solve for x in each case

--------------------------------
Answer:

So our solutions are

or

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