math calculus
posted by Shreya .
(24x^354x^215x)/(6x^215x)
i don't factor number from whole equation way i do it is find number that add to give me 54 and multiply to give 360. the number i get 60 and +6.
so i do this:
24x^360x+6x15x i factor this further and get 12x(2x^25)3x(25)/(3x)(2x5)
nothing be cancelling now.

(24x^354x^215x)/(6x^215x)
= 3x(8x^2  18x  5)/(3x(2x  5) )
= 3x(2x5)(4x + 1)/(3x(2x5) )
= 4x+1 
thanks but i tell before that i not factor that way i not pull out common number from whole equation i do the longer way i find number that add to give me 54 and multiply to give me 360. numbers i get are 60 and +6. doing this way i should also get right answer but i not getting it i want to know why?

The method you describe is used to factor quadratics.
Your numerator is not a quadratic , it is a cubic, so you MUST factor out x to start this.
Besides that 3 is also a common factor of the top. 
but my teacher show me that way.
24x^360x+6x15x
by doing this i shall also get same answer.
i break down between 60x and +6x. so it all become this:
24x^360x
and if i factor this down further then it be 12x(2x^25)
6x15x
if i factor this down more then it be 3x(2x5)
so all together it be
12x(2x^25)3x(25)/3x(2x5)
i need help right here. this part because i not able to cancel anything off but 3x's. 
You are very confused.
The method you show works only for quadatics.
As I stated above you have a cubic
so let's look at 24x^3  54x^2  15x
You should ALWAYS look for a common factor before you do anything else, so
3x(8x^2  18x  5)
now for the quadratic part:......
multiply 8x(5) to get 40
what two numbers multiply to get 40 and add to get 18
they are 20 and +2
so 8x^2  20x + 2x  5
= 4x(2x  5) + 1(2x  5)
= (2x5)(4x+1)
and with the 3x in front, we have
3x(2x5)(4x+1) as I had before
In this method you MUST get the same binomial in each part, you did not even get close to that.
Your answer does not make any sense at all, why don't you expand it and see if you get back the original?
If you show what you did to your teacher, he/she will agree with me that it is wrong. 
sorry reiny for so much trouble sorry by cubic i thought u mean we couldn't factor down the equation any further i did not realize cubic meant ^3 sorry now i understand and get so well thank you very much for taking your time explaining all this :)

You are welcome