SOLUTION: I was wondering if you could show me how to factor this equation: 7a2+53a+28 This is the work I got to but then I could go no father. I used the x-box to find the answer. Af

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I was wondering if you could show me how to factor this equation: 7a2+53a+28 This is the work I got to but then I could go no father. I used the x-box to find the answer. Af      Log On


   

Question 245969: I was wondering if you could show me how to factor this equation: 7a2+53a+28
This is the work I got to but then I could go no father.
I used the x-box to find the answer.
After the x-box I got
(a+7)(7a+7)
7a2+56a+28 which does not equal the original question.
(when it says 7a2 it means 7 times a squared)
Found 3 solutions by jim_thompson5910, solver91311, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 7a%5E2%2B53a%2B28, we can see that the first coefficient is 7, the second coefficient is 53, and the last term is 28.


Now multiply the first coefficient 7 by the last term 28 to get %287%29%2828%29=196.


Now the question is: what two whole numbers multiply to 196 (the previous product) and add to the second coefficient 53?


To find these two numbers, we need to list all of the factors of 196 (the previous product).


Factors of 196:
1,2,4,7,14,28,49,98,196
-1,-2,-4,-7,-14,-28,-49,-98,-196


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


These factors pair up and multiply to 196.
1*196 = 196
2*98 = 196
4*49 = 196
7*28 = 196
14*14 = 196
(-1)*(-196) = 196
(-2)*(-98) = 196
(-4)*(-49) = 196
(-7)*(-28) = 196
(-14)*(-14) = 196

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 53:


First NumberSecond NumberSum
11961+196=197
2982+98=100
4494+49=53
7287+28=35
141414+14=28
-1-196-1+(-196)=-197
-2-98-2+(-98)=-100
-4-49-4+(-49)=-53
-7-28-7+(-28)=-35
-14-14-14+(-14)=-28



From the table, we can see that the two numbers 4 and 49 add to 53 (the middle coefficient).


So the two numbers 4 and 49 both multiply to 196 and add to 53


Now replace the middle term 53a with 4a%2B49a. Remember, 4 and 49 add to 53. So this shows us that 4a%2B49a=53a.


7a%5E2%2Bhighlight%284a%2B49a%29%2B28 Replace the second term 53a with 4a%2B49a.


%287a%5E2%2B4a%29%2B%2849a%2B28%29 Group the terms into two pairs.


a%287a%2B4%29%2B%2849a%2B28%29 Factor out the GCF a from the first group.


a%287a%2B4%29%2B7%287a%2B4%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.


%28a%2B7%29%287a%2B4%29 Combine like terms. Or factor out the common term 7a%2B4


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Answer:


So 7a%5E2%2B53a%2B28 factors to %28a%2B7%29%287a%2B4%29.


In other words, 7a%5E2%2B53a%2B28=%28a%2B7%29%287a%2B4%29.


Note: you can check the answer by expanding %28a%2B7%29%287a%2B4%29 to get 7a%5E2%2B53a%2B28 or by graphing the original expression and the answer (the two graphs should be identical).

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Go back and check your x-box, whatever that is.

Lead coefficient.

First degree coefficient.

Constant term.


John

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
factor this expression:
7a^2+53a+28
7a^2+49a+4a+28
7a(a+7)+4(a+7)
(a+7)(7a+4)
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Cheers,
Stan H.