SOLUTION: 8c^2 + 38c + 35 factor

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Question 925883: 8c^2 + 38c + 35 factor
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 8c%5E2%2B38c%2B35, we can see that the first coefficient is 8, the second coefficient is 38, and the last term is 35.


Now multiply the first coefficient 8 by the last term 35 to get %288%29%2835%29=280.


Now the question is: what two whole numbers multiply to 280 (the previous product) and add to the second coefficient 38?


To find these two numbers, we need to list all of the factors of 280 (the previous product).


Factors of 280:
1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
-1,-2,-4,-5,-7,-8,-10,-14,-20,-28,-35,-40,-56,-70,-140,-280


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


These factors pair up and multiply to 280.
1*280 = 280
2*140 = 280
4*70 = 280
5*56 = 280
7*40 = 280
8*35 = 280
10*28 = 280
14*20 = 280
(-1)*(-280) = 280
(-2)*(-140) = 280
(-4)*(-70) = 280
(-5)*(-56) = 280
(-7)*(-40) = 280
(-8)*(-35) = 280
(-10)*(-28) = 280
(-14)*(-20) = 280

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 38:


First NumberSecond NumberSum
12801+280=281
21402+140=142
4704+70=74
5565+56=61
7407+40=47
8358+35=43
102810+28=38
142014+20=34
-1-280-1+(-280)=-281
-2-140-2+(-140)=-142
-4-70-4+(-70)=-74
-5-56-5+(-56)=-61
-7-40-7+(-40)=-47
-8-35-8+(-35)=-43
-10-28-10+(-28)=-38
-14-20-14+(-20)=-34



From the table, we can see that the two numbers 10 and 28 add to 38 (the middle coefficient).


So the two numbers 10 and 28 both multiply to 280 and add to 38


Now replace the middle term 38c with 10c%2B28c. Remember, 10 and 28 add to 38. So this shows us that 10c%2B28c=38c.


8c%5E2%2Bhighlight%2810c%2B28c%29%2B35 Replace the second term 38c with 10c%2B28c.


%288c%5E2%2B10c%29%2B%2828c%2B35%29 Group the terms into two pairs.


2c%284c%2B5%29%2B%2828c%2B35%29 Factor out the GCF 2c from the first group.


2c%284c%2B5%29%2B7%284c%2B5%29 Factor out 7 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.


%282c%2B7%29%284c%2B5%29 Combine like terms. Or factor out the common term 4c%2B5


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Answer:


So 8c%5E2%2B38c%2B35 factors to %282c%2B7%29%284c%2B5%29.


In other words, 8c%5E2%2B38c%2B35=%282c%2B7%29%284c%2B5%29.


Note: you can check the answer by expanding %282c%2B7%29%284c%2B5%29 to get 8c%5E2%2B38c%2B35 or by graphing the original expression and the answer (the two graphs should be identical).