SOLUTION: These need to be factored completely 30z^8 + 44z^5 +16z^2 Could it be 2z^2(3z^ + 2)(5z^3 +4) 24x� + 14xy +2y� (m+n)(x+3) + (m+n)(5+5) Could it be (m+n+3)(x

Question 181934: These need to be factored completely
30z^8 + 44z^5 +16z^2 Could it be 2z^2(3z^ + 2)(5z^3 +4)
24x� + 14xy +2y�
(m+n)(x+3) + (m+n)(5+5) Could it be (m+n+3)(x+y+5)
Solve using the principal of zero products
(x+ 1/7)(x-4/5) = 0
Find the x-intercepts for the graph of the equation
Y = x� + 4x -45 Could it be (-9,0,(5,0)
Factor by grouping
-36x� -30x + 36 Could it be -6(3x-2)(2x+3)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two, which will hopefully help you with the rest of the problems. If not, then repost.

# 1

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 15 and 8 respectively.

Now multiply the first coefficient 15 and the last coefficient 8 to get 120. Now what two numbers multiply to 120 and add to the middle coefficient 22? Let's list all of the factors of 120:

Factors of 120:
1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

-1,-2,-3,-4,-5,-6,-8,-10,-12,-15,-20,-24,-30,-40,-60,-120 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 120
1*120
2*60
3*40
4*30
5*24
6*20
8*15
10*12
(-1)*(-120)
(-2)*(-60)
(-3)*(-40)
(-4)*(-30)
(-5)*(-24)
(-6)*(-20)
(-8)*(-15)
(-10)*(-12)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 22? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 22

First Number	Second Number	Sum
1	120	1+120=121
2	60	2+60=62
3	40	3+40=43
4	30	4+30=34
5	24	5+24=29
6	20	6+20=26
8	15	8+15=23
10	12	10+12=22
-1	-120	-1+(-120)=-121
-2	-60	-2+(-60)=-62
-3	-40	-3+(-40)=-43
-4	-30	-4+(-30)=-34
-5	-24	-5+(-24)=-29
-6	-20	-6+(-20)=-26
-8	-15	-8+(-15)=-23
-10	-12	-10+(-12)=-22

From this list we can see that 10 and 12 add up to 22 and multiply to 120

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

# 2

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 12 and 1 respectively.

Now multiply the first coefficient 12 and the last coefficient 1 to get 12. Now what two numbers multiply to 12 and add to the middle coefficient 7? Let's list all of the factors of 12:

Factors of 12:
1,2,3,4,6,12

-1,-2,-3,-4,-6,-12 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 12
1*12
2*6
3*4
(-1)*(-12)
(-2)*(-6)
(-3)*(-4)

note: remember two negative numbers multiplied together make a positive 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	12	1+12=13
2	6	2+6=8
3	4	3+4=7
-1	-12	-1+(-12)=-13
-2	-6	-2+(-6)=-8
-3	-4	-3+(-4)=-7

From this list we can see that 3 and 4 add up to 7 and multiply to 12

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

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