Question

How do you divide `(18n ^ { 6} + 24n ^ { 5} + 4n ^ { 4} ) \div 6n ^ { 2}`?

Answer 1

Divide each term by `6n^2` separately in order to final answer of `3n^4+4n^3+2/3` `n^2`

Explanation:

Think of this question in terms of creating a fraction. In other words, `(18n^6 + 24n^5 + 4n^4)/(6n^2)` . (The line in a fraction means the same thing as `÷` ... divide).

Just like any fraction, you can separate the terms in the numerator by placing each term over the denominator like this:

`(18n^6)/(6n^2) + (24n^5)/(6n^2) + (4n^4)/(6n^2)`

Now work on each term separately.

1st term : `(18n^6)/(6n^2)` --> `18/6=(6*3)/(6*1)=3/1=3` and `n^6/n^2=n^(6-2)=n^4`. So the 1st term `=3n^4`
2nd term : `(24n^5)/(6n^2)` --> `24/6=(6*4)/(6*1)=4/1=4` and `n^5/n^2=n^(5-2)=n^3`. So the 2nd term is `4n^3`
3rd term: `(4n^4)/(6n^2)` --> `4/6=(2*2)/(2*3)=2/3` and `n^4/n^2=n^(4-2)=n^2`. So the 3rd term is `2/3` `n^2`

Now put these terms back together to get the final answer

`3n^4+4n^3+2/3` `n^2`

Quick tip: Once you understand this method, try solving these problem in your head by simply taking it one step at a time.

Answer 2

Begin by dividing out the `n^2`, then the 6.

Explanation:

When you take out the `n^2`, you are left with `(18n^2+24n^3+4n^2)/6`.
From here you are able to divide all terms by two, due to this being the least common denominator,
This results in`(18n^2+24n^3+4n^2)/3`.