SOLUTION: Please help me solve this problem 2b^2+13b-7

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Question 157254This question is from textbook algebra 2
: Please help me solve this problem 2b^2+13b-7 This question is from textbook algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to factor this?




Looking at the expression 2b%5E2%2B13b-7, we can see that the first coefficient is 2, the second coefficient is 13, and the last term is -7.


Now multiply the first coefficient 2 by the last term -7 to get %282%29%28-7%29=-14.


Now the question is: what two whole numbers multiply to -14 (the previous product) and add to the second coefficient 13?


To find these two numbers, we need to list all of the factors of -14 (the previous product).


Factors of -14:
1,2,7,14
-1,-2,-7,-14


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


These factors pair up and multiply to -14.
1*(-14)
2*(-7)
(-1)*(14)
(-2)*(7)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 13:


First NumberSecond NumberSum
1-141+(-14)=-13
2-72+(-7)=-5
-114-1+14=13
-27-2+7=5



From the table, we can see that the two numbers -1 and 14 add to 13 (the middle coefficient).


So the two numbers -1 and 14 both multiply to -14 and add to 13


Now replace the middle term 13b with -b%2B14b. Remember, -1 and 14 add to 13. So this shows us that -b%2B14b=13b.


2b%5E2%2Bhighlight%28-b%2B14b%29-7 Replace the second term 13b with -b%2B14b.


%282b%5E2-b%29%2B%2814b-7%29 Group the terms into two pairs.


b%282b-1%29%2B%2814b-7%29 Factor out the GCF b from the first group.


b%282b-1%29%2B7%282b-1%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.


%28b%2B7%29%282b-1%29 Combine like terms. Or factor out the common term 2b-1

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Answer:


So 2b%5E2%2B13b-7 factors to %28b%2B7%29%282b-1%29.


In other words, 2b%5E2%2B13b-7=%28b%2B7%29%282b-1%29


Note: you can check the answer by FOILing %28b%2B7%29%282b-1%29 to get 2b%5E2%2B13b-7 or by graphing the original expression and the answer (the two graphs should be identical).



Questions? Email me at jim_thompson5910@hotmail.com (note: the space is really an underscore)