SOLUTION: Could you please help with this problem? Factor the expression. 6q^2+4q-2

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Question 207250This question is from textbook
: Could you please help with this problem? Factor the expression. 6q^2+4q-2 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


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6q%5E2%2B4q-2 Start with the given expression.


2%283q%5E2%2B2q-1%29 Factor out the GCF 2.


Now let's try to factor the inner expression 3q%5E2%2B2q-1


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Looking at the expression 3q%5E2%2B2q-1, we can see that the first coefficient is 3, the second coefficient is 2, and the last term is -1.


Now multiply the first coefficient 3 by the last term -1 to get %283%29%28-1%29=-3.


Now the question is: what two whole numbers multiply to -3 (the previous product) and add to the second coefficient 2?


To find these two numbers, we need to list all of the factors of -3 (the previous product).


Factors of -3:
1,3
-1,-3


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


These factors pair up and multiply to -3.
1*(-3) = -3
(-1)*(3) = -3

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 2:


First NumberSecond NumberSum
1-31+(-3)=-2
-13-1+3=2



From the table, we can see that the two numbers -1 and 3 add to 2 (the middle coefficient).


So the two numbers -1 and 3 both multiply to -3 and add to 2


Now replace the middle term 2q with -q%2B3q. Remember, -1 and 3 add to 2. So this shows us that -q%2B3q=2q.


3q%5E2%2Bhighlight%28-q%2B3q%29-1 Replace the second term 2q with -q%2B3q.


%283q%5E2-q%29%2B%283q-1%29 Group the terms into two pairs.


q%283q-1%29%2B%283q-1%29 Factor out the GCF q from the first group.


q%283q-1%29%2B1%283q-1%29 Factor out 1 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.


%28q%2B1%29%283q-1%29 Combine like terms. Or factor out the common term 3q-1


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So 2%283q%5E2%2B2q-1%29 then factors further to 2%28q%2B1%29%283q-1%29


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Answer:


So 6q%5E2%2B4q-2 completely factors to 2%28q%2B1%29%283q-1%29.


In other words, 6q%5E2%2B4q-2=2%28q%2B1%29%283q-1%29.


Note: you can check the answer by expanding 2%28q%2B1%29%283q-1%29 to get 6q%5E2%2B4q-2 or by graphing the original expression and the answer (the two graphs should be identical).

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