Question 143269: 4x^2 + 34x + 42
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Do you want to factor?
 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 2 and 21 respectively.
Now multiply the first coefficient 2 and the last coefficient 21 to get 42. Now what two numbers multiply to 42 and add to the middle coefficient 17? Let's list all of the factors of 42:
Factors of 42:
1,2,3,6,7,14,21,42
-1,-2,-3,-6,-7,-14,-21,-42 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 42
1*42
2*21
3*14
6*7
(-1)*(-42)
(-2)*(-21)
(-3)*(-14)
(-6)*(-7)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 17? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 17
| First Number | Second Number | Sum | | 1 | 42 | 1+42=43 | | 2 | 21 | 2+21=23 | | 3 | 14 | 3+14=17 | | 6 | 7 | 6+7=13 | | -1 | -42 | -1+(-42)=-43 | | -2 | -21 | -2+(-21)=-23 | | -3 | -14 | -3+(-14)=-17 | | -6 | -7 | -6+(-7)=-13 |
From this list we can see that 3 and 14 add up to 17 and multiply to 42
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
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