# math calculus

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(24x^3-54x^2-15x)/(6x^2-15x)

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^3-60x+6x-15x i factor this further and get 12x(2x^2-5)3x(2-5)/(3x)(2x-5)

nothing be cancelling now.

• math calculus -

(24x^3-54x^2-15x)/(6x^2-15x)
= 3x(8x^2 - 18x - 5)/(3x(2x - 5) )
= 3x(2x-5)(4x + 1)/(3x(2x-5) )
= 4x+1

• math calculus -

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?

• math calculus -

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.

• math calculus -

but my teacher show me that way.

24x^3-60x+6x-15x

by doing this i shall also get same answer.

i break down between -60x and +6x. so it all become this:

24x^3-60x

and if i factor this down further then it be 12x(2x^2-5)

6x-15x

if i factor this down more then it be 3x(2x-5)

so all together it be

12x(2x^2-5)3x(2-5)/3x(2x-5)

i need help right here. this part because i not able to cancel anything off but 3x's.

• math calculus -

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)

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)
= (2x-5)(4x+1)

and with the 3x in front, we have

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.

• math calculus -

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 :)

• math calculus -

You are welcome