SOLUTION: Factor completely 3x^2 + 30x + 75

Question 189835: Factor completely
3x^2 + 30x + 75
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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 1 and 25 respectively.

Now multiply the first coefficient 1 and the last coefficient 25 to get 25. Now what two numbers multiply to 25 and add to the middle coefficient 10? Let's list all of the factors of 25:

Factors of 25:
1,5

-1,-5 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 25
1*25
5*5
(-1)*(-25)
(-5)*(-5)

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

Now which of these pairs add to 10? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 10

First Number	Second Number	Sum
1	25	1+25=26
5	5	5+5=10
-1	-25	-1+(-25)=-26
-5	-5	-5+(-5)=-10

From this list we can see that 5 and 5 add up to 10 and multiply to 25

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 )

note: is equivalent to since the term occurs twice. So also factors to

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So factors down to

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Answer:

So completely factors to
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