SOLUTION: Can -4w(w^2+4w-5) be factored?

Question 119782: Can -4w(w^2+4w-5) be factored?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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 -5 respectively.

Now multiply the first coefficient 1 and the last coefficient -5 to get -5. Now what two numbers multiply to -5 and add to the middle coefficient 4? Let's list all of the factors of -5:

Factors of -5:
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 -5
(1)*(-5)
(-1)*(5)

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

Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4

First Number	Second Number	Sum
1	-5	1+(-5)=-4
-1	5	-1+5=4

From this list we can see that -1 and 5 add up to 4 and multiply to -5

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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Now reintroduce the outer term

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Answer:

So factors to

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