SOLUTION: Factor 2x^2+3x-5

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Question 191767: Factor
2x^2+3x-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 2x%5E2%2B3x-5, we can see that the first coefficient is 2, the second coefficient is 3, and the last term is -5.


Now multiply the first coefficient 2 by the last term -5 to get %282%29%28-5%29=-10.


Now the question is: what two whole numbers multiply to -10 (the previous product) and add to the second coefficient 3?


To find these two numbers, we need to list all of the factors of -10 (the previous product).


Factors of -10:
1,2,5,10
-1,-2,-5,-10


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


These factors pair up and multiply to -10.
1*(-10)
2*(-5)
(-1)*(10)
(-2)*(5)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 3:


First NumberSecond NumberSum
1-101+(-10)=-9
2-52+(-5)=-3
-110-1+10=9
-25-2+5=3



From the table, we can see that the two numbers -2 and 5 add to 3 (the middle coefficient).


So the two numbers -2 and 5 both multiply to -10 and add to 3


Now replace the middle term 3x with -2x%2B5x. Remember, -2 and 5 add to 3. So this shows us that -2x%2B5x=3x.


2x%5E2%2Bhighlight%28-2x%2B5x%29-5 Replace the second term 3x with -2x%2B5x.


%282x%5E2-2x%29%2B%285x-5%29 Group the terms into two pairs.


2x%28x-1%29%2B%285x-5%29 Factor out the GCF 2x from the first group.


2x%28x-1%29%2B5%28x-1%29 Factor out 5 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.


%282x%2B5%29%28x-1%29 Combine like terms. Or factor out the common term x-1

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Answer:


So 2x%5E2%2B3x-5 factors to %282x%2B5%29%28x-1%29.


Note: you can check the answer by FOILing %282x%2B5%29%28x-1%29 to get 2x%5E2%2B3x-5 or by graphing the original expression and the answer (the two graphs should be identical).