Answer:
3
Step-by-step explanation:
2x
8
3y
Given the following question:
First expression:
![\begin{gathered} \frac{12x^3-14x^2+16x-8}{3x-2} \\ \text{ Factor the expression:} \\ 12x^3-14x^2+16x-8=2(6x^3-7x^2+8x-4) \\ \frac{2\left(6x^3-7x^2+8x-4\right)}{3x-2} \\ \text{ Factor:} \\ 2\left(6x^3-7x^2+8x-4\right)=(3x-2)(2x^2-x+2) \\ =(3x-2)(2x^2-x+2)=2\left(3x-2\right)\left(2x^2-x+2\right) \\ \frac{2\left(3x-2\right)\left(2x^2-x+2\right)}{3x-2} \\ \text{ Cancel the common factor:} \\ -(3x-2) \\ 4x^2-2x+4 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B12x%5E3-14x%5E2%2B16x-8%7D%7B3x-2%7D%20%5C%5C%20%5Ctext%7B%20Factor%20the%20expression%3A%7D%20%5C%5C%2012x%5E3-14x%5E2%2B16x-8%3D2%286x%5E3-7x%5E2%2B8x-4%29%20%5C%5C%20%5Cfrac%7B2%5Cleft%286x%5E3-7x%5E2%2B8x-4%5Cright%29%7D%7B3x-2%7D%20%5C%5C%20%5Ctext%7B%20Factor%3A%7D%20%5C%5C%202%5Cleft%286x%5E3-7x%5E2%2B8x-4%5Cright%29%3D%283x-2%29%282x%5E2-x%2B2%29%20%5C%5C%20%3D%283x-2%29%282x%5E2-x%2B2%29%3D2%5Cleft%283x-2%5Cright%29%5Cleft%282x%5E2-x%2B2%5Cright%29%20%5C%5C%20%5Cfrac%7B2%5Cleft%283x-2%5Cright%29%5Cleft%282x%5E2-x%2B2%5Cright%29%7D%7B3x-2%7D%20%5C%5C%20%5Ctext%7B%20Cancel%20the%20common%20factor%3A%7D%20%5C%5C%20-%283x-2%29%20%5C%5C%204x%5E2-2x%2B4%20%5Cend%7Bgathered%7D)
Second expression:
4 - 1/x (16)-1/x 2
4x-18/x
This is a combination in which you choose 4 from 10.
The formula is
combinations = 10! / 4! * (10-4)!
combinations = 10! / 4! * 6!
combinations = 10 * 9 * 8 * 7 * 6! / 4! * 6!
combinations = 10 * 9 * 8 * 7 / 4 * 3 * 2
combinations = 10 * 3 * 7
combinations = 210
Source:
http://www.1728.org/combinat.htm