SOLUTION: I need to completely factor the trinomial x^2+2x-35. I've tried to figure it out myself and every time I get a different answer. Then I tried a solver and it said it couldn't be f

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need to completely factor the trinomial x^2+2x-35. I've tried to figure it out myself and every time I get a different answer. Then I tried a solver and it said it couldn't be f      Log On


   

Question 452947: I need to completely factor the trinomial x^2+2x-35.
I've tried to figure it out myself and every time I get a different answer. Then I tried a solver and it said it couldn't be factored and that's not even one of the choices in my homework. It asks for an answer or whether the polynomial is prime. I'm so confused. Can someone help?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression x%5E2%2B2x-35, we can see that the first coefficient is 1, the second coefficient is 2, and the last term is -35.


Now multiply the first coefficient 1 by the last term -35 to get %281%29%28-35%29=-35.


Now the question is: what two whole numbers multiply to -35 (the previous product) and add to the second coefficient 2?


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 2:


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 -5 and 7 add to 2 (the middle coefficient).


So the two numbers -5 and 7 both multiply to -35 and add to 2


Now replace the middle term 2x with -5x%2B7x. Remember, -5 and 7 add to 2. So this shows us that -5x%2B7x=2x.


x%5E2%2Bhighlight%28-5x%2B7x%29-35 Replace the second term 2x with -5x%2B7x.


%28x%5E2-5x%29%2B%287x-35%29 Group the terms into two pairs.


x%28x-5%29%2B%287x-35%29 Factor out the GCF x from the first group.


x%28x-5%29%2B7%28x-5%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%2B7%29%28x-5%29 Combine like terms. Or factor out the common term x-5


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Answer:


So x%5E2%2B2x-35 factors to %28x%2B7%29%28x-5%29.


In other words, x%5E2%2B2x-35=%28x%2B7%29%28x-5%29.


Note: you can check the answer by expanding %28x%2B7%29%28x-5%29 to get x%5E2%2B2x-35 or by graphing the original expression and the answer (the two graphs should be identical).