SOLUTION: 35y^3-60y^2-20y Factor the trinomial completely

Question 191479: 35y^3-60y^2-20y
Factor the trinomial completely
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

------------------------------------------------------------

Looking at we can see that the first term is and the last term is where the coefficients are 7 and -4 respectively.

Now multiply the first coefficient 7 and the last coefficient -4 to get -28. Now what two numbers multiply to -28 and add to the middle coefficient -12? Let's list all of the factors of -28:

Factors of -28:
1,2,4,7,14,28

-1,-2,-4,-7,-14,-28 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -28
(1)*(-28)
(2)*(-14)
(4)*(-7)
(-1)*(28)
(-2)*(14)
(-4)*(7)

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

Now which of these pairs add to -12? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -12

First Number	Second Number	Sum
1	-28	1+(-28)=-27
2	-14	2+(-14)=-12
4	-7	4+(-7)=-3
-1	28	-1+28=27
-2	14	-2+14=12
-4	7	-4+7=3

From this list we can see that 2 and -14 add up to -12 and multiply to -28

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 )

------------------------------------------------------------

So our expression goes from and factors further to

------------------
Answer:

So completely factors to

RELATED QUESTIONS
completely factor the given polynomials 10y^3 - 10y^2 -... (answered by ewatrrr)

Factor the trinomials completely..... 4x^3+18x^2+18x= Factor completely... (answered by nerdybill)

factor completely:... (answered by jim_thompson5910,Earlsdon)

Completely factor the polynomial 3x*3+12x*2+3x+12 Factor the trinomial completely... (answered by lynnlo,Alan3354)

Factor the trinomial. {{{c^3-5c^2-24c}}} Factor... (answered by robertb)

50x^3+95x^2+30x Factor the trinomial... (answered by jim_thompson5910)

16p^4-88p^3+121p^2 Factor the trinomial completely (answered by user_dude2008)

factor the trinomial completely... (answered by RedemptiveMath)

factor the trinomial completely... (answered by stanbon)