Question 115207This question is from textbook Beginning Algebra
: Rewrite the middle term as the sum of two terms and then factor completely.
4z squared -18z squared -10z
This question is from textbook Beginning Algebra
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 4 and -10 respectively.
Now multiply the first coefficient 4 and the last coefficient -10 to get -40. Now what two numbers multiply to -40 and add to the middle coefficient -18? Let's list all of the factors of -40:
Factors of -40:
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -40
(1)*(-40)
(2)*(-20)
(4)*(-10)
(5)*(-8)
(-1)*(40)
(-2)*(20)
(-4)*(10)
(-5)*(8)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -18? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -18
| First Number | Second Number | Sum | | 1 | -40 | 1+(-40)=-39 | | 2 | -20 | 2+(-20)=-18 | | 4 | -10 | 4+(-10)=-6 | | 5 | -8 | 5+(-8)=-3 | | -1 | 40 | -1+40=39 | | -2 | 20 | -2+20=18 | | -4 | 10 | -4+10=6 | | -5 | 8 | -5+8=3 |
From this list we can see that 2 and -20 add up to -18 and multiply to -40
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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Answer:
So factors to
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