SOLUTION: Yes hello, I'm stuck on a polynomial expression. I need to factor a polynomial expression: 2x^2(squared)-7x-4. Please help? Thanks.

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Question 778022: Yes hello, I'm stuck on a polynomial expression. I need to factor a polynomial expression: 2x^2(squared)-7x-4. Please help? Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 2x%5E2-7x-4, we can see that the first coefficient is 2, the second coefficient is -7, and the last term is -4.


Now multiply the first coefficient 2 by the last term -4 to get %282%29%28-4%29=-8.


Now the question is: what two whole numbers multiply to -8 (the previous product) and add to the second coefficient -7?


To find these two numbers, we need to list all of the factors of -8 (the previous product).


Factors of -8:
1,2,4,8
-1,-2,-4,-8


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


These factors pair up and multiply to -8.
1*(-8) = -8
2*(-4) = -8
(-1)*(8) = -8
(-2)*(4) = -8

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -7:


First NumberSecond NumberSum
1-81+(-8)=-7
2-42+(-4)=-2
-18-1+8=7
-24-2+4=2



From the table, we can see that the two numbers 1 and -8 add to -7 (the middle coefficient).


So the two numbers 1 and -8 both multiply to -8 and add to -7


Now replace the middle term -7x with x-8x. Remember, 1 and -8 add to -7. So this shows us that x-8x=-7x.


2x%5E2%2Bhighlight%28x-8x%29-4 Replace the second term -7x with x-8x.


%282x%5E2%2Bx%29%2B%28-8x-4%29 Group the terms into two pairs.


x%282x%2B1%29%2B%28-8x-4%29 Factor out the GCF x from the first group.


x%282x%2B1%29-4%282x%2B1%29 Factor out 4 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-4%29%282x%2B1%29 Combine like terms. Or factor out the common term 2x%2B1


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Answer:


So 2x%5E2-7x-4 factors to %28x-4%29%282x%2B1%29.


In other words, 2x%5E2-7x-4=%28x-4%29%282x%2B1%29.


Note: you can check the answer by expanding %28x-4%29%282x%2B1%29 to get 2x%5E2-7x-4 or by graphing the original expression and the answer (the two graphs should be identical).