SOLUTION: p^2 + 11p + 10

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Question 610467: p^2 + 11p + 10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression p%5E2%2B11p%2B10, we can see that the first coefficient is 1, the second coefficient is 11, and the last term is 10.


Now multiply the first coefficient 1 by the last term 10 to get %281%29%2810%29=10.


Now the question is: what two whole numbers multiply to 10 (the previous product) and add to the second coefficient 11?


To find these two numbers, we need to list all of the factors of 10 (the previous product).


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


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


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

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 11:


First NumberSecond NumberSum
1101+10=11
252+5=7
-1-10-1+(-10)=-11
-2-5-2+(-5)=-7



From the table, we can see that the two numbers 1 and 10 add to 11 (the middle coefficient).


So the two numbers 1 and 10 both multiply to 10 and add to 11


Now replace the middle term 11p with p%2B10p. Remember, 1 and 10 add to 11. So this shows us that p%2B10p=11p.


p%5E2%2Bhighlight%28p%2B10p%29%2B10 Replace the second term 11p with p%2B10p.


%28p%5E2%2Bp%29%2B%2810p%2B10%29 Group the terms into two pairs.


p%28p%2B1%29%2B%2810p%2B10%29 Factor out the GCF p from the first group.


p%28p%2B1%29%2B10%28p%2B1%29 Factor out 10 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%2B10%29%28p%2B1%29 Combine like terms. Or factor out the common term p%2B1


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Answer:


So p%5E2%2B11p%2B10 factors to %28p%2B10%29%28p%2B1%29.


In other words, p%5E2%2B11p%2B10=%28p%2B10%29%28p%2B1%29.


Note: you can check the answer by expanding %28p%2B10%29%28p%2B1%29 to get p%5E2%2B11p%2B10 or by graphing the original expression and the answer (the two graphs should be identical).

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