SOLUTION: 46. Factor completely. -3t^3+ 3t^2-6t 60. Factor polynomial completely. 10a^2+ab-2b^2 80. Factor completely. 4m^2+20m+25 90. Factor each polynomial completely, given tha

Question 181957: 46. Factor completely. -3t^3+ 3t^2-6t

60. Factor polynomial completely. 10a^2+ab-2b^2
80. Factor completely. 4m^2+20m+25
90. Factor each polynomial completely, given that the binomial Following it is a factor of the polynomial. x^3-4x^2-3x-10, x-5
102. Solve each equation. t2+1=13/6t

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first three to get you started:

# 46

Start with the given expression

Factor out the GCF

So factors to

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# 60

Looking at we can see that the first term is and the last term is where the coefficients are 10 and -2 respectively.

Now multiply the first coefficient 10 and the last coefficient -2 to get -20. Now what two numbers multiply to -20 and add to the middle coefficient 1? Let's list all of the factors of -20:

Factors of -20:
1,2,4,5,10,20

-1,-2,-4,-5,-10,-20 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -20
(1)*(-20)
(2)*(-10)
(4)*(-5)
(-1)*(20)
(-2)*(10)
(-4)*(5)

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

Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1

First Number	Second Number	Sum
1	-20	1+(-20)=-19
2	-10	2+(-10)=-8
4	-5	4+(-5)=-1
-1	20	-1+20=19
-2	10	-2+10=8
-4	5	-4+5=1

From this list we can see that -4 and 5 add up to 1 and multiply to -20

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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# 80

Looking at we can see that the first term is and the last term is where the coefficients are 4 and 25 respectively.

Now multiply the first coefficient 4 and the last coefficient 25 to get 100. Now what two numbers multiply to 100 and add to the middle coefficient 20? Let's list all of the factors of 100:

Factors of 100:
1,2,4,5,10,20,25,50

-1,-2,-4,-5,-10,-20,-25,-50 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 100
1*100
2*50
4*25
5*20
10*10
(-1)*(-100)
(-2)*(-50)
(-4)*(-25)
(-5)*(-20)
(-10)*(-10)

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

Now which of these pairs add to 20? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 20

First Number	Second Number	Sum
1	100	1+100=101
2	50	2+50=52
4	25	4+25=29
5	20	5+20=25
10	10	10+10=20
-1	-100	-1+(-100)=-101
-2	-50	-2+(-50)=-52
-4	-25	-4+(-25)=-29
-5	-20	-5+(-20)=-25
-10	-10	-10+(-10)=-20

From this list we can see that 10 and 10 add up to 20 and multiply to 100

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 )

note: is equivalent to since the term occurs twice. So also factors to

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

Answer:
So factors to

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