SOLUTION: The number of hot dogs sold at the concession stand during each hour h after opening at a s0ccer tournament is given by the polynomial 2h^2-19h+24. write this polonomial in factore

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: The number of hot dogs sold at the concession stand during each hour h after opening at a s0ccer tournament is given by the polynomial 2h^2-19h+24. write this polonomial in factore      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 376723: The number of hot dogs sold at the concession stand during each hour h after opening at a s0ccer tournament is given by the polynomial 2h^2-19h+24. write this polonomial in factored form.
Any help will be helpful dont understand the book.
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 2h%5E2-19h%2B24, we can see that the first coefficient is 2, the second coefficient is -19, and the last term is 24.


Now multiply the first coefficient 2 by the last term 24 to get %282%29%2824%29=48.


Now the question is: what two whole numbers multiply to 48 (the previous product) and add to the second coefficient -19?


To find these two numbers, we need to list all of the factors of 48 (the previous product).


Factors of 48:
1,2,3,4,6,8,12,16,24,48
-1,-2,-3,-4,-6,-8,-12,-16,-24,-48


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


These factors pair up and multiply to 48.
1*48 = 48
2*24 = 48
3*16 = 48
4*12 = 48
6*8 = 48
(-1)*(-48) = 48
(-2)*(-24) = 48
(-3)*(-16) = 48
(-4)*(-12) = 48
(-6)*(-8) = 48

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -19:


First NumberSecond NumberSum
1481+48=49
2242+24=26
3163+16=19
4124+12=16
686+8=14
-1-48-1+(-48)=-49
-2-24-2+(-24)=-26
-3-16-3+(-16)=-19
-4-12-4+(-12)=-16
-6-8-6+(-8)=-14



From the table, we can see that the two numbers -3 and -16 add to -19 (the middle coefficient).


So the two numbers -3 and -16 both multiply to 48 and add to -19


Now replace the middle term -19h with -3h-16h. Remember, -3 and -16 add to -19. So this shows us that -3h-16h=-19h.


2h%5E2%2Bhighlight%28-3h-16h%29%2B24 Replace the second term -19h with -3h-16h.


%282h%5E2-3h%29%2B%28-16h%2B24%29 Group the terms into two pairs.


h%282h-3%29%2B%28-16h%2B24%29 Factor out the GCF h from the first group.


h%282h-3%29-8%282h-3%29 Factor out 8 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.


%28h-8%29%282h-3%29 Combine like terms. Or factor out the common term 2h-3


===============================================================


Answer:


So 2h%5E2-19h%2B24 factors to %28h-8%29%282h-3%29.


In other words, 2h%5E2-19h%2B24=%28h-8%29%282h-3%29.


Note: you can check the answer by expanding %28h-8%29%282h-3%29 to get 2h%5E2-19h%2B24 or by graphing the original expression and the answer (the two graphs should be identical).



If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim