SOLUTION: Factor the trinomial. 4x^2-56x-92 I'm having problems figuring out this problem. The only numbers I can find that go into 92 are 4 and 23 but when I plug that in: 4x(-23)+4x=

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the trinomial. 4x^2-56x-92 I'm having problems figuring out this problem. The only numbers I can find that go into 92 are 4 and 23 but when I plug that in: 4x(-23)+4x=      Log On


   

Question 701292: Factor the trinomial. 4x^2-56x-92
I'm having problems figuring out this problem. The only numbers I can find that go into 92 are 4 and 23 but when I plug that in:
4x(-23)+4x= -92x+4x=-88x. So it's not equaling -56x. I'm not sure what I'm doing wrong? Any help would be greatly appreciated! Thank you.
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-56x-92 Start with the given expression.


4%28x%5E2-14x-23%29 Factor out the GCF 4.


Now let's try to factor the inner expression x%5E2-14x-23


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Looking at the expression x%5E2-14x-23, we can see that the first coefficient is 1, the second coefficient is -14, and the last term is -23.


Now multiply the first coefficient 1 by the last term -23 to get %281%29%28-23%29=-23.


Now the question is: what two whole numbers multiply to -23 (the previous product) and add to the second coefficient -14?


To find these two numbers, we need to list all of the factors of -23 (the previous product).


Factors of -23:
1,23
-1,-23


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


These factors pair up and multiply to -23.
1*(-23) = -23
(-1)*(23) = -23

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -14:


First NumberSecond NumberSum
1-231+(-23)=-22
-123-1+23=22



From the table, we can see that there are no pairs of numbers which add to -14. So x%5E2-14x-23 cannot be factored.


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Answer:


So 4x%5E2-56x-92 simply factors to 4%28x%5E2-14x-23%29


In other words, 4x%5E2-56x-92=4%28x%5E2-14x-23%29.

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-56x-92..... write -92 as 196-288

4x%5E2-56x%2B196-288....group first three terms together
%284x%5E2-56x%2B196%29-288....factor out 4
4%28x%5E2-14x%2B49%29-288....note that x%5E2-14x%2B49=%28x-7%29%5E2
4%28x-7%29%5E2-288