SOLUTION: Factor the following 3z^2-10z-25
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Question 142171: Factor the following 3z^2-10z-25
Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
(3z+5)(z-5)
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 -25 respectively.
Now multiply the first coefficient 3 and the last coefficient -25 to get -75. Now what two numbers multiply to -75 and add to the middle coefficient -10? Let's list all of the factors of -75:
Factors of -75:
1,3,5,15,25,75
-1,-3,-5,-15,-25,-75 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -75
(1)*(-75)
(3)*(-25)
(5)*(-15)
(-1)*(75)
(-3)*(25)
(-5)*(15)
note: remember, the product of a negative and a positive number is a negative 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 | -75 | 1+(-75)=-74 |
| 3 | -25 | 3+(-25)=-22 |
| 5 | -15 | 5+(-15)=-10 |
| -1 | 75 | -1+75=74 |
| -3 | 25 | -3+25=22 |
| -5 | 15 | -5+15=10 |
From this list we can see that 5 and -15 add up to -10 and multiply to -75
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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