SOLUTION: Solve the equation 3x2 - 15x = 0. 6x2 - 5x = 6 Factor the expression x2 - 8xy + 12y2 completely. Choose one factor of the following expression from the list b

Question 147136: Solve the equation 3x2 - 15x = 0.

6x2 - 5x = 6

Factor the expression x2 - 8xy + 12y2 completely.

Choose one factor of the following expression from the list below.
6x2 - 5x - 4

Thanks for the help and i will also put a donation for you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1: Solve the equation 3x2 - 15x = 0.

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So our answers are or

# 2: Solve the equation 6x2 - 5x = 6

Start with the given equation.

Get all terms to the left side.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So our answers are or

# 3: Factor the expression x2 - 8xy + 12y2 completely.

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 12 respectively.

Now multiply the first coefficient 1 and the last coefficient 12 to get 12. Now what two numbers multiply to 12 and add to the middle coefficient -8? 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 -8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -8

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 -2 and -6 add up to -8 and multiply to 12

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

# 4: Choose one factor of the following expression from the list below.
6x2 - 5x - 4

Looking at we can see that the first term is and the last term is where the coefficients are 6 and -4 respectively.

Now multiply the first coefficient 6 and the last coefficient -4 to get -24. Now what two numbers multiply to -24 and add to the middle coefficient -5? Let's list all of the factors of -24:

Factors of -24:
1,2,3,4,6,8,12,24

-1,-2,-3,-4,-6,-8,-12,-24 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -24
(1)*(-24)
(2)*(-12)
(3)*(-8)
(4)*(-6)
(-1)*(24)
(-2)*(12)
(-3)*(8)
(-4)*(6)

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

Now which of these pairs add to -5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -5

First Number	Second Number	Sum
1	-24	1+(-24)=-23
2	-12	2+(-12)=-10
3	-8	3+(-8)=-5
4	-6	4+(-6)=-2
-1	24	-1+24=23
-2	12	-2+12=10
-3	8	-3+8=5
-4	6	-4+6=2

From this list we can see that 3 and -8 add up to -5 and multiply to -24

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 )

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

Answer:
So factors to

So you could either choose or
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