SOLUTION: I need help trying to solve this problem. Thank you in advance, for helping me out. I really appreciate your time and efforts. Have a terrific day :) Here is the question? Choose t

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: I need help trying to solve this problem. Thank you in advance, for helping me out. I really appreciate your time and efforts. Have a terrific day :) Here is the question? Choose t      Log On


   

Question 915746: I need help trying to solve this problem. Thank you in advance, for helping me out. I really appreciate your time and efforts. Have a terrific day :) Here is the question? Choose the correct method to factor each of the following:
6t^2 - 18t - 24
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6t%5E2-18t-24 Start with the given expression.


6%28t%5E2-3t-4%29 Factor out the GCF 6.


Now let's try to factor the inner expression t%5E2-3t-4


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Looking at the expression t%5E2-3t-4, we can see that the first coefficient is 1, the second coefficient is -3, and the last term is -4.


Now multiply the first coefficient 1 by the last term -4 to get %281%29%28-4%29=-4.


Now the question is: what two whole numbers multiply to -4 (the previous product) and add to the second coefficient -3?


To find these two numbers, we need to list all of the factors of -4 (the previous product).


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


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


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

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -3:


First NumberSecond NumberSum
1-41+(-4)=-3
2-22+(-2)=0
-14-1+4=3
-22-2+2=0



From the table, we can see that the two numbers 1 and -4 add to -3 (the middle coefficient).


So the two numbers 1 and -4 both multiply to -4 and add to -3


Now replace the middle term -3t with t-4t. Remember, 1 and -4 add to -3. So this shows us that t-4t=-3t.


t%5E2%2Bhighlight%28t-4t%29-4 Replace the second term -3t with t-4t.


%28t%5E2%2Bt%29%2B%28-4t-4%29 Group the terms into two pairs.


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


t%28t%2B1%29-4%28t%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.


%28t-4%29%28t%2B1%29 Combine like terms. Or factor out the common term t%2B1


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So 6%28t%5E2-3t-4%29 then factors further to 6%28t-4%29%28t%2B1%29


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Answer:


So 6t%5E2-18t-24 completely factors to 6%28t-4%29%28t%2B1%29.


In other words, 6t%5E2-18t-24=6%28t-4%29%28t%2B1%29.


Note: you can check the answer by expanding 6%28t-4%29%28t%2B1%29 to get 6t%5E2-18t-24 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