SOLUTION: 24x^2-37-5 my teacher taugt us lIke multi:AC then subtract to get -37 0k so 24*5=120 then she said see what all goes into that number then when u found it see if it is the same

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 24x^2-37-5 my teacher taugt us lIke multi:AC then subtract to get -37 0k so 24*5=120 then she said see what all goes into that number then when u found it see if it is the same      Log On


   

Question 188535: 24x^2-37-5
my teacher taugt us lIke multi:AC then subtract to get -37
0k so 24*5=120 then she said see what all goes into that number
then when u found it see if it is the same is B which is -37..
i got -40+3 is -37
but when i put it all together
24x^2-40x+3x-5
4x(6x-10)+1(3x-5) and Its suppose to be the same
i get lost can u help me im hopin u can understand wat im sayin
thats the best way i can explain it
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 24x%5E2-37x-5, we can see that the first coefficient is 24, the second coefficient is -37, and the last term is -5.


Now multiply the first coefficient 24 by the last term -5 to get %2824%29%28-5%29=-120.


Now the question is: what two whole numbers multiply to -120 (the previous product) and add to the second coefficient -37?


To find these two numbers, we need to list all of the factors of -120 (the previous product).


Factors of -120:
1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
-1,-2,-3,-4,-5,-6,-8,-10,-12,-15,-20,-24,-30,-40,-60,-120


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


These factors pair up and multiply to -120.
1*(-120)
2*(-60)
3*(-40)
4*(-30)
5*(-24)
6*(-20)
8*(-15)
10*(-12)
(-1)*(120)
(-2)*(60)
(-3)*(40)
(-4)*(30)
(-5)*(24)
(-6)*(20)
(-8)*(15)
(-10)*(12)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -37:


First NumberSecond NumberSum
1-1201+(-120)=-119
2-602+(-60)=-58
3-403+(-40)=-37
4-304+(-30)=-26
5-245+(-24)=-19
6-206+(-20)=-14
8-158+(-15)=-7
10-1210+(-12)=-2
-1120-1+120=119
-260-2+60=58
-340-3+40=37
-430-4+30=26
-524-5+24=19
-620-6+20=14
-815-8+15=7
-1012-10+12=2



From the table, we can see that the two numbers 3 and -40 add to -37 (the middle coefficient).


So the two numbers 3 and -40 both multiply to -120 and add to -37


Now replace the middle term -37x with 3x-40x. Remember, 3 and -40 add to -37. So this shows us that 3x-40x=-37x.


24x%5E2%2Bhighlight%283x-40x%29-5 Replace the second term -37x with 3x-40x.


%2824x%5E2%2B3x%29%2B%28-40x-5%29 Group the terms into two pairs.


3x%288x%2B1%29%2B%28-40x-5%29 Factor out the GCF 3x from the first group.


3x%288x%2B1%29-5%288x%2B1%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.


%283x-5%29%288x%2B1%29 Combine like terms. Or factor out the common term 8x%2B1

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Answer:


So 24x%5E2-37x-5 factors to %283x-5%29%288x%2B1%29.


Note: you can check the answer by FOILing %283x-5%29%288x%2B1%29 to get 24x%5E2-37x-5 or by graphing the original expression and the answer (the two graphs should be identical).