SOLUTION: what is 2y to the third minus 7y squared minus 15y factored?

Question 150701: what is 2y to the third minus 7y squared minus 15y factored?
Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Factor:
Notice that every term has a factor of y, so you can factor a y.
Now look at the trinomial in parentheses.
The first term can be factored as and the last term has factors of:
-15 = -1*15 or 1(-15)
-15 = -3*5 or 3(-5)
To get the middle coefficient of -7, do 2*(-5)+1(3) = -10+3 = -7
So you can try:
...and this works.
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 2 and -15 respectively.

Now multiply the first coefficient 2 and the last coefficient -15 to get -30. Now what two numbers multiply to -30 and add to the middle coefficient -7? Let's list all of the factors of -30:

Factors of -30:
1,2,3,5,6,10,15,30

-1,-2,-3,-5,-6,-10,-15,-30 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -30
(1)*(-30)
(2)*(-15)
(3)*(-10)
(5)*(-6)
(-1)*(30)
(-2)*(15)
(-3)*(10)
(-5)*(6)

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

Now which of these pairs add to -7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -7

First Number Second Number Sum
1 -30 1+(-30)=-29
2 -15 2+(-15)=-13
3 -10 3+(-10)=-7
5 -6 5+(-6)=-1
-1 30 -1+30=29
-2 15 -2+15=13
-3 10 -3+10=7
-5 6 -5+6=1

From this list we can see that 3 and -10 add up to -7 and multiply to -30

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

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First Number	Second Number	Sum
1	-30	1+(-30)=-29
2	-15	2+(-15)=-13
3	-10	3+(-10)=-7
5	-6	5+(-6)=-1
-1	30	-1+30=29
-2	15	-2+15=13
-3	10	-3+10=7
-5	6	-5+6=1