SOLUTION: factor complete : 7x^2 + 33x - 10 = 0

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Question 912772: factor complete : 7x^2 + 33x - 10 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 7x%5E2%2B33x-10, we can see that the first coefficient is 7, the second coefficient is 33, and the last term is -10.


Now multiply the first coefficient 7 by the last term -10 to get %287%29%28-10%29=-70.


Now the question is: what two whole numbers multiply to -70 (the previous product) and add to the second coefficient 33?


To find these two numbers, we need to list all of the factors of -70 (the previous product).


Factors of -70:
1,2,5,7,10,14,35,70
-1,-2,-5,-7,-10,-14,-35,-70


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


These factors pair up and multiply to -70.
1*(-70) = -70
2*(-35) = -70
5*(-14) = -70
7*(-10) = -70
(-1)*(70) = -70
(-2)*(35) = -70
(-5)*(14) = -70
(-7)*(10) = -70

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 33:


First NumberSecond NumberSum
1-701+(-70)=-69
2-352+(-35)=-33
5-145+(-14)=-9
7-107+(-10)=-3
-170-1+70=69
-235-2+35=33
-514-5+14=9
-710-7+10=3



From the table, we can see that the two numbers -2 and 35 add to 33 (the middle coefficient).


So the two numbers -2 and 35 both multiply to -70 and add to 33


Now replace the middle term 33x with -2x%2B35x. Remember, -2 and 35 add to 33. So this shows us that -2x%2B35x=33x.


7x%5E2%2Bhighlight%28-2x%2B35x%29-10 Replace the second term 33x with -2x%2B35x.


%287x%5E2-2x%29%2B%2835x-10%29 Group the terms into two pairs.


x%287x-2%29%2B%2835x-10%29 Factor out the GCF x from the first group.


x%287x-2%29%2B5%287x-2%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.


%28x%2B5%29%287x-2%29 Combine like terms. Or factor out the common term 7x-2


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Answer:


So 7x%5E2%2B33x-10 factors to %28x%2B5%29%287x-2%29.


In other words, 7x%5E2%2B33x-10=%28x%2B5%29%287x-2%29.


Note: you can check the answer by expanding %28x%2B5%29%287x-2%29 to get 7x%5E2%2B33x-10 or by graphing the original expression and the answer (the two graphs should be identical).


Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim