SOLUTION: 5x^2-34x-7

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 5x^2-34x-7      Log On


   

Question 483520: 5x^2-34x-7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 5x%5E2-34x-7, we can see that the first coefficient is 5, the second coefficient is -34, and the last term is -7.


Now multiply the first coefficient 5 by the last term -7 to get %285%29%28-7%29=-35.


Now the question is: what two whole numbers multiply to -35 (the previous product) and add to the second coefficient -34?


To find these two numbers, we need to list all of the factors of -35 (the previous product).


Factors of -35:
1,5,7,35
-1,-5,-7,-35


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


These factors pair up and multiply to -35.
1*(-35) = -35
5*(-7) = -35
(-1)*(35) = -35
(-5)*(7) = -35

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -34:


First NumberSecond NumberSum
1-351+(-35)=-34
5-75+(-7)=-2
-135-1+35=34
-57-5+7=2



From the table, we can see that the two numbers 1 and -35 add to -34 (the middle coefficient).


So the two numbers 1 and -35 both multiply to -35 and add to -34


Now replace the middle term -34x with x-35x. Remember, 1 and -35 add to -34. So this shows us that x-35x=-34x.


5x%5E2%2Bhighlight%28x-35x%29-7 Replace the second term -34x with x-35x.


%285x%5E2%2Bx%29%2B%28-35x-7%29 Group the terms into two pairs.


x%285x%2B1%29%2B%28-35x-7%29 Factor out the GCF x from the first group.


x%285x%2B1%29-7%285x%2B1%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.


%28x-7%29%285x%2B1%29 Combine like terms. Or factor out the common term 5x%2B1


===============================================================


Answer:


So 5x%5E2-34x-7 factors to %28x-7%29%285x%2B1%29.


In other words, 5x%5E2-34x-7=%28x-7%29%285x%2B1%29.


Note: you can check the answer by expanding %28x-7%29%285x%2B1%29 to get 5x%5E2-34x-7 or by graphing the original expression and the answer (the two graphs should be identical).