SOLUTION: -2x2 + 3x + 20

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Question 585441: -2x2 + 3x + 20
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.



-2x%5E2%2B3x%2B20 Start with the given expression.


-%282x%5E2-3x-20%29 Factor out the GCF -1.


Now let's try to factor the inner expression 2x%5E2-3x-20


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Looking at the expression 2x%5E2-3x-20, we can see that the first coefficient is 2, the second coefficient is -3, and the last term is -20.


Now multiply the first coefficient 2 by the last term -20 to get %282%29%28-20%29=-40.


Now the question is: what two whole numbers multiply to -40 (the previous product) and add to the second coefficient -3?


To find these two numbers, we need to list all of the factors of -40 (the previous product).


Factors of -40:
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40


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


These factors pair up and multiply to -40.
1*(-40) = -40
2*(-20) = -40
4*(-10) = -40
5*(-8) = -40
(-1)*(40) = -40
(-2)*(20) = -40
(-4)*(10) = -40
(-5)*(8) = -40

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -3:


First NumberSecond NumberSum
1-401+(-40)=-39
2-202+(-20)=-18
4-104+(-10)=-6
5-85+(-8)=-3
-140-1+40=39
-220-2+20=18
-410-4+10=6
-58-5+8=3



From the table, we can see that the two numbers 5 and -8 add to -3 (the middle coefficient).


So the two numbers 5 and -8 both multiply to -40 and add to -3


Now replace the middle term -3x with 5x-8x. Remember, 5 and -8 add to -3. So this shows us that 5x-8x=-3x.


2x%5E2%2Bhighlight%285x-8x%29-20 Replace the second term -3x with 5x-8x.


%282x%5E2%2B5x%29%2B%28-8x-20%29 Group the terms into two pairs.


x%282x%2B5%29%2B%28-8x-20%29 Factor out the GCF x from the first group.


x%282x%2B5%29-4%282x%2B5%29 Factor out 4 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.


%28x-4%29%282x%2B5%29 Combine like terms. Or factor out the common term 2x%2B5


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So -%282x%5E2-3x-20%29 then factors further to -%28x-4%29%282x%2B5%29


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Answer:


So -2x%5E2%2B3x%2B20 completely factors to -%28x-4%29%282x%2B5%29.


In other words, -2x%5E2%2B3x%2B20=-%28x-4%29%282x%2B5%29.


Note: you can check the answer by expanding -%28x-4%29%282x%2B5%29 to get -2x%5E2%2B3x%2B20 or by graphing the original expression and the answer (the two graphs should be identical).

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