SOLUTION: 4x^3+8x^2-12x

Question 257119: 4x^3+8x^2-12x
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 -3 respectively.

Now multiply the first coefficient 1 and the last coefficient -3 to get -3. Now what two numbers multiply to -3 and add to the middle coefficient 2? Let's list all of the factors of -3:

Factors of -3:
1,3

-1,-3 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -3
(1)*(-3)
(-1)*(3)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2

First Number	Second Number	Sum
1	-3	1+(-3)=-2
-1	3	-1+3=2

From this list we can see that -1 and 3 add up to 2 and multiply to -3

Now looking at the expression , replace with (notice combines back 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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