SOLUTION: I need to learn how to factor completly 3x^2 + 17x + 10

Question 118105: I need to learn how to factor completly
3x^2 + 17x + 10
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 3 and 10 respectively.

Now multiply the first coefficient 3 and the last coefficient 10 to get 30. Now what two numbers multiply to 30 and add to the middle coefficient 17? 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 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	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 2 and 15 add up to 17 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 )

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

So factors to

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