SOLUTION: 5x^2-26x+5= 15x^3-9x^2-6x= 64a^4-224a^2=196=

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Question 251548: 5x^2-26x+5=
15x^3-9x^2-6x=
64a^4-224a^2=196=
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started




Looking at the expression 5x%5E2-26x%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 = 25
5*5 = 25
(-1)*(-25) = 25
(-5)*(-5) = 25

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 -26x with -x-25x. Remember, -1 and -25 add to -26. So this shows us that -x-25x=-26x.


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


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


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


x%285x-1%29-5%285x-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.


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


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Answer:


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


In other words, 5x%5E2-26x%2B5=%28x-5%29%285x-1%29.


Note: you can check the answer by expanding %28x-5%29%285x-1%29 to get 5x%5E2-26x%2B5 or by graphing the original expression and the answer (the two graphs should be identical).