Question

What is `(6x^{4} - 5x^{3} - 18x^{2} - 5x + 2) -:( 3x + 22)`?

Answer 1

`2x^3-(49x^2)/3+(1024x)/9-22573/27+496660/(27(3x+22))`

Explanation:

This is quite long and I hope you can follow this through.

`(6x^4)/(3x)=2x^3` (this is our first term)

`2x^3(3x+22)=6x^4+44x^2`

`6x^4-5x^3-18x^2-5x+2-(6x^4+44x^2)=6x^4-5x^3-18x^2-5x+2-6x^4-44x^2=-49x^3-18x^2-5x+2`

`-(49x^3)/(3x)=-(49x^2)/3` (this is our second term)

`-(49x^2)/3(3x+22)=-(49x^2)/3-(1078x^2)/3`

`-49x^3-18x^2-5x+2-(-(49x^2)/3-(1078x^2)/3)=-49x^3-18x^2-5x+2+(49x^2)/3+(1078x^2)/3=(1024x^2)/3-5x+2`

`((1024x^2)/3)/(3x)=(1024x)/9` (this is our third term)

`(1024x)/9(3x+22)=(1024x^2)/3+(22528x)/9`

`(1024x^2)/3-5x+2-((1024x^2)/3+(22528x)/9)=(1024x^2)/3-5x+2-(1024x^2)/3-(22528x)/9=-(22573x)/9+2`

`-((22573x)/9)/(3x)=-22573/27` (this is our fourth term)

`-22573/27(3x+22)=-(22573x)/27-496606/27`

`-(22573x)/9+2-(-(22573x)/27-496606/27)=-(22573x)/9+2+(22573x)/27+496606/27=496660/27`

`496660/(27(3x+22))` (this is our final term)

This gives us:
`2x^3-(49x^2)/3+(1024x)/9-22573/27+496660/(27(3x+22))`