SOLUTION: Factor 2y^2-7y-49

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Question 103997This question is from textbook beginning and intermediate algebra
: Factor
2y^2-7y-49
This question is from textbook beginning and intermediate algebra

Found 2 solutions by edjones, jim_thompson5910:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
2y^2-7y-49
(y-7)(2y+7)
Ed

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression 2y%5E2-7y-49, we can see that the first coefficient is 2, the second coefficient is -7, and the last term is -49.



Now multiply the first coefficient 2 by the last term -49 to get %282%29%28-49%29=-98.



Now the question is: what two whole numbers multiply to -98 (the previous product) and add to the second coefficient -7?



To find these two numbers, we need to list all of the factors of -98 (the previous product).



Factors of -98:

1,2,7,14,49,98

-1,-2,-7,-14,-49,-98



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



These factors pair up and multiply to -98.

1*(-98) = -98
2*(-49) = -98
7*(-14) = -98
(-1)*(98) = -98
(-2)*(49) = -98
(-7)*(14) = -98


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



First NumberSecond NumberSum
1-981+(-98)=-97
2-492+(-49)=-47
7-147+(-14)=-7
-198-1+98=97
-249-2+49=47
-714-7+14=7




From the table, we can see that the two numbers 7 and -14 add to -7 (the middle coefficient).



So the two numbers 7 and -14 both multiply to -98 and add to -7



Now replace the middle term -7y with 7y-14y. Remember, 7 and -14 add to -7. So this shows us that 7y-14y=-7y.



2y%5E2%2Bhighlight%287y-14y%29-49 Replace the second term -7y with 7y-14y.



%282y%5E2%2B7y%29%2B%28-14y-49%29 Group the terms into two pairs.



y%282y%2B7%29%2B%28-14y-49%29 Factor out the GCF y from the first group.



y%282y%2B7%29-7%282y%2B7%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.



%28y-7%29%282y%2B7%29 Combine like terms. Or factor out the common term 2y%2B7



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Answer:



So 2%2Ay%5E2-7%2Ay-49 factors to %28y-7%29%282y%2B7%29.



In other words, 2%2Ay%5E2-7%2Ay-49=%28y-7%29%282y%2B7%29.



Note: you can check the answer by expanding %28y-7%29%282y%2B7%29 to get 2%2Ay%5E2-7%2Ay-49 or by graphing the original expression and the answer (the two graphs should be identical).