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
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Answer:
So our solutions are
or
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