SOLUTION: factor complety 5a*2-26a+5

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Question 195725: factor complety
5a*2-26a+5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: use ^ for exponent instead of *




Looking at the expression 5a%5E2-26a%2B5, we can see that the first coefficient is 5, the second coefficient is -26, and the last term is 5.


Now multiply the first coefficient 5 by the last term 5 to get %285%29%285%29=25.


Now the question is: what two whole numbers multiply to 25 (the previous product) and add to the second coefficient -26?


To find these two numbers, we need to list all of the factors of 25 (the previous product).


Factors of 25:
1,5,25
-1,-5,-25


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


These factors pair up and multiply to 25.
1*25
5*5
(-1)*(-25)
(-5)*(-5)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -26:


First NumberSecond NumberSum
1251+25=26
555+5=10
-1-25-1+(-25)=-26
-5-5-5+(-5)=-10



From the table, we can see that the two numbers -1 and -25 add to -26 (the middle coefficient).


So the two numbers -1 and -25 both multiply to 25 and add to -26


Now replace the middle term -26a with -a-25a. Remember, -1 and -25 add to -26. So this shows us that -a-25a=-26a.


5a%5E2%2Bhighlight%28-a-25a%29%2B5 Replace the second term -26a with -a-25a.


%285a%5E2-a%29%2B%28-25a%2B5%29 Group the terms into two pairs.


a%285a-1%29%2B%28-25a%2B5%29 Factor out the GCF a from the first group.


a%285a-1%29-5%285a-1%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.


%28a-5%29%285a-1%29 Combine like terms. Or factor out the common term 5a-1

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Answer:


So 5a%5E2-26a%2B5 factors to %28a-5%29%285a-1%29.