SOLUTION: Dear sir or mam: I am working on factoring trinomials completely 4p^2-16p-20

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Question 207732: Dear sir or mam:
I am working on factoring trinomials completely
4p^2-16p-20
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


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4p%5E2-16p-20 Start with the given expression.


4%28p%5E2-4p-5%29 Factor out the GCF 4.


Now let's try to factor the inner expression p%5E2-4p-5


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Looking at the expression p%5E2-4p-5, we can see that the first coefficient is 1, the second coefficient is -4, and the last term is -5.


Now multiply the first coefficient 1 by the last term -5 to get %281%29%28-5%29=-5.


Now the question is: what two whole numbers multiply to -5 (the previous product) and add to the second coefficient -4?


To find these two numbers, we need to list all of the factors of -5 (the previous product).


Factors of -5:
1,5
-1,-5


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


These factors pair up and multiply to -5.
1*(-5) = -5
(-1)*(5) = -5

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -4:


First NumberSecond NumberSum
1-51+(-5)=-4
-15-1+5=4



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


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


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


p%5E2%2Bhighlight%28p-5p%29-5 Replace the second term -4p with p-5p.


%28p%5E2%2Bp%29%2B%28-5p-5%29 Group the terms into two pairs.


p%28p%2B1%29%2B%28-5p-5%29 Factor out the GCF p from the first group.


p%28p%2B1%29-5%28p%2B1%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.


%28p-5%29%28p%2B1%29 Combine like terms. Or factor out the common term p%2B1


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So 4%28p%5E2-4p-5%29 then factors further to 4%28p-5%29%28p%2B1%29


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Answer:


So 4p%5E2-16p-20 completely factors to 4%28p-5%29%28p%2B1%29.


In other words, 4p%5E2-16p-20=4%28p-5%29%28p%2B1%29.


Note: you can check the answer by expanding 4%28p-5%29%28p%2B1%29 to get 4p%5E2-16p-20 or by graphing the original expression and the answer (the two graphs should be identical).

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