Answer: Its factored form will be
![6n(n-1)(n^2-3n-3)](https://tex.z-dn.net/?f=6n%28n-1%29%28n%5E2-3n-3%29)
Step-by-step explanation:
Since we have given that
![6n^4-24n^3+18n](https://tex.z-dn.net/?f=6n%5E4-24n%5E3%2B18n)
So, we need to factor ,
![6n(n^3-4n^2+3)](https://tex.z-dn.net/?f=6n%28n%5E3-4n%5E2%2B3%29)
Now,
![\text{Let }p(n)=n^3-4n^2+3](https://tex.z-dn.net/?f=%5Ctext%7BLet%20%7Dp%28n%29%3Dn%5E3-4n%5E2%2B3)
Now, by hit and trial method, we put n=1,
![p(1)=1^3-4\times1^2+3=1-4+3=1-1=0](https://tex.z-dn.net/?f=p%281%29%3D1%5E3-4%5Ctimes1%5E2%2B3%3D1-4%2B3%3D1-1%3D0)
![n=1\\n-1=0](https://tex.z-dn.net/?f=n%3D1%5C%5Cn-1%3D0)
So, n-1 is also factor of p(n).
Now,
![\frac{n^3-4n^2+3}{n-1}=n^2-3n-3](https://tex.z-dn.net/?f=%5Cfrac%7Bn%5E3-4n%5E2%2B3%7D%7Bn-1%7D%3Dn%5E2-3n-3)
So, its factored form will be
![6n(n-1)(n^2-3n-3)](https://tex.z-dn.net/?f=6n%28n-1%29%28n%5E2-3n-3%29)
There are 72 different ways the director can fill the positions.
(1+2+3+4+5+6+7+8) x 2
You multiply it by 2 because there are going to be 4 other people who will not have a position, and 8/4 is 2.
13 units.
Since both are negative, and they’re just asking for distance between, you can just subtract 12 from 25 to get 13.
Answer:
Step-by-step explanation:
A complete circle has 360 degrees
So
300 + 32 + b = 360 Combine the left
332 + b = 360 Subtract 332 from both sides
b = 360 - 332
b = 28