SOLUTION: please help me with this problem? 4x^3 - 10x^2 - 50x Thanks.

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Question 678307: please help me with this problem?
4x^3 - 10x^2 - 50x
Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E3-10x%5E2-50x Start with the given expression.


2x%282x%5E2-5x-25%29 Factor out the GCF 2x.


Now let's try to factor the inner expression 2x%5E2-5x-25


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Looking at the expression 2x%5E2-5x-25, we can see that the first coefficient is 2, the second coefficient is -5, and the last term is -25.


Now multiply the first coefficient 2 by the last term -25 to get %282%29%28-25%29=-50.


Now the question is: what two whole numbers multiply to -50 (the previous product) and add to the second coefficient -5?


To find these two numbers, we need to list all of the factors of -50 (the previous product).


Factors of -50:
1,2,5,10,25,50
-1,-2,-5,-10,-25,-50


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


These factors pair up and multiply to -50.
1*(-50) = -50
2*(-25) = -50
5*(-10) = -50
(-1)*(50) = -50
(-2)*(25) = -50
(-5)*(10) = -50

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -5:


First NumberSecond NumberSum
1-501+(-50)=-49
2-252+(-25)=-23
5-105+(-10)=-5
-150-1+50=49
-225-2+25=23
-510-5+10=5



From the table, we can see that the two numbers 5 and -10 add to -5 (the middle coefficient).


So the two numbers 5 and -10 both multiply to -50 and add to -5


Now replace the middle term -5x with 5x-10x. Remember, 5 and -10 add to -5. So this shows us that 5x-10x=-5x.


2x%5E2%2Bhighlight%285x-10x%29-25 Replace the second term -5x with 5x-10x.


%282x%5E2%2B5x%29%2B%28-10x-25%29 Group the terms into two pairs.


x%282x%2B5%29%2B%28-10x-25%29 Factor out the GCF x from the first group.


x%282x%2B5%29-5%282x%2B5%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.


%28x-5%29%282x%2B5%29 Combine like terms. Or factor out the common term 2x%2B5


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So 2x%282x%5E2-5x-25%29 then factors further to 2x%28x-5%29%282x%2B5%29


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Answer:


So 4x%5E3-10x%5E2-50x completely factors to 2x%28x-5%29%282x%2B5%29.


In other words, 4x%5E3-10x%5E2-50x=2x%28x-5%29%282x%2B5%29.


Note: you can check the answer by expanding 2x%28x-5%29%282x%2B5%29 to get 4x%5E3-10x%5E2-50x or by graphing the original expression and the answer (the two graphs should be identical).