SOLUTION: factor please -6x^2+3x+30 factor please thanks so much@!

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Question 297092: factor please -6x^2+3x+30 factor please thanks so much@!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-6x%5E2%2B3x%2B30 Start with the given expression.


-3%282x%5E2-x-10%29 Factor out the GCF -3.


Now let's try to factor the inner expression 2x%5E2-x-10


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Looking at the expression 2x%5E2-x-10, we can see that the first coefficient is 2, the second coefficient is -1, and the last term is -10.


Now multiply the first coefficient 2 by the last term -10 to get %282%29%28-10%29=-20.


Now the question is: what two whole numbers multiply to -20 (the previous product) and add to the second coefficient -1?


To find these two numbers, we need to list all of the factors of -20 (the previous product).


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


Note: list the negative of each factor. This will allow us to find all possible combinations.


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

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -1:


First NumberSecond NumberSum
1-201+(-20)=-19
2-102+(-10)=-8
4-54+(-5)=-1
-120-1+20=19
-210-2+10=8
-45-4+5=1



From the table, we can see that the two numbers 4 and -5 add to -1 (the middle coefficient).


So the two numbers 4 and -5 both multiply to -20 and add to -1


Now replace the middle term -1x with 4x-5x. Remember, 4 and -5 add to -1. So this shows us that 4x-5x=-1x.


2x%5E2%2Bhighlight%284x-5x%29-10 Replace the second term -1x with 4x-5x.


%282x%5E2%2B4x%29%2B%28-5x-10%29 Group the terms into two pairs.


2x%28x%2B2%29%2B%28-5x-10%29 Factor out the GCF 2x from the first group.


2x%28x%2B2%29-5%28x%2B2%29 Factor out 5 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%282x-5%29%28x%2B2%29 Combine like terms. Or factor out the common term x%2B2


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So -3%282x%5E2-x-10%29 then factors further to -3%282x-5%29%28x%2B2%29


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Answer:


So -6x%5E2%2B3x%2B30 completely factors to -3%282x-5%29%28x%2B2%29.


In other words, -6x%5E2%2B3x%2B30=-3%282x-5%29%28x%2B2%29.


Note: you can check the answer by expanding -3%282x-5%29%28x%2B2%29 to get -6x%5E2%2B3x%2B30 or by graphing the original expression and the answer (the two graphs should be identical).