SOLUTION: 20x^2-41x+20=

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Question 336539: 20x^2-41x+20=
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 20x%5E2-41x%2B20, we can see that the first coefficient is 20, the second coefficient is -41, and the last term is 20.


Now multiply the first coefficient 20 by the last term 20 to get %2820%29%2820%29=400.


Now the question is: what two whole numbers multiply to 400 (the previous product) and add to the second coefficient -41?


To find these two numbers, we need to list all of the factors of 400 (the previous product).


Factors of 400:
1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
-1,-2,-4,-5,-8,-10,-16,-20,-25,-40,-50,-80,-100,-200,-400


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


These factors pair up and multiply to 400.
1*400 = 400
2*200 = 400
4*100 = 400
5*80 = 400
8*50 = 400
10*40 = 400
16*25 = 400
20*20 = 400
(-1)*(-400) = 400
(-2)*(-200) = 400
(-4)*(-100) = 400
(-5)*(-80) = 400
(-8)*(-50) = 400
(-10)*(-40) = 400
(-16)*(-25) = 400
(-20)*(-20) = 400

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -41:


First NumberSecond NumberSum
14001+400=401
22002+200=202
41004+100=104
5805+80=85
8508+50=58
104010+40=50
162516+25=41
202020+20=40
-1-400-1+(-400)=-401
-2-200-2+(-200)=-202
-4-100-4+(-100)=-104
-5-80-5+(-80)=-85
-8-50-8+(-50)=-58
-10-40-10+(-40)=-50
-16-25-16+(-25)=-41
-20-20-20+(-20)=-40



From the table, we can see that the two numbers -16 and -25 add to -41 (the middle coefficient).


So the two numbers -16 and -25 both multiply to 400 and add to -41


Now replace the middle term -41x with -16x-25x. Remember, -16 and -25 add to -41. So this shows us that -16x-25x=-41x.


20x%5E2%2Bhighlight%28-16x-25x%29%2B20 Replace the second term -41x with -16x-25x.


%2820x%5E2-16x%29%2B%28-25x%2B20%29 Group the terms into two pairs.


4x%285x-4%29%2B%28-25x%2B20%29 Factor out the GCF 4x from the first group.


4x%285x-4%29-5%285x-4%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.


%284x-5%29%285x-4%29 Combine like terms. Or factor out the common term 5x-4


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Answer:


So 20x%5E2-41x%2B20 factors to %284x-5%29%285x-4%29.


In other words, 20x%5E2-41x%2B20=%284x-5%29%285x-4%29.


Note: you can check the answer by expanding %284x-5%29%285x-4%29 to get 20x%5E2-41x%2B20 or by graphing the original expression and the answer (the two graphs should be identical).


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim