SOLUTION: factor completely: 6y^3+11y^2-35y
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Question 131051: factor completely: 6y^3+11y^2-35y
Found 2 solutions by jim_thompson5910, Earlsdon:
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 6 and -35 respectively.
Now multiply the first coefficient 6 and the last coefficient -35 to get -210. Now what two numbers multiply to -210 and add to the middle coefficient 11? Let's list all of the factors of -210:
Factors of -210:
1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
-1,-2,-3,-5,-6,-7,-10,-14,-15,-21,-30,-35,-42,-70,-105,-210 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -210
(1)*(-210)
(2)*(-105)
(3)*(-70)
(5)*(-42)
(6)*(-35)
(7)*(-30)
(10)*(-21)
(14)*(-15)
(-1)*(210)
(-2)*(105)
(-3)*(70)
(-5)*(42)
(-6)*(35)
(-7)*(30)
(-10)*(21)
(-14)*(15)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 11
| First Number | Second Number | Sum | | 1 | -210 | 1+(-210)=-209 |
| 2 | -105 | 2+(-105)=-103 |
| 3 | -70 | 3+(-70)=-67 |
| 5 | -42 | 5+(-42)=-37 |
| 6 | -35 | 6+(-35)=-29 |
| 7 | -30 | 7+(-30)=-23 |
| 10 | -21 | 10+(-21)=-11 |
| 14 | -15 | 14+(-15)=-1 |
| -1 | 210 | -1+210=209 |
| -2 | 105 | -2+105=103 |
| -3 | 70 | -3+70=67 |
| -5 | 42 | -5+42=37 |
| -6 | 35 | -6+35=29 |
| -7 | 30 | -7+30=23 |
| -10 | 21 | -10+21=11 |
| -14 | 15 | -14+15=1 |
From this list we can see that -10 and 21 add up to 11 and multiply to -210
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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So our expression goes from and factors further to
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Answer:
So factors to
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Factor:
First, factor a y.
Now factor the trinomial.
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