SOLUTION: 4x^2 + 34x + 42

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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