The given polynomial is:
![18cd^2+12c^2d+9cd](https://tex.z-dn.net/?f=18cd%5E2%2B12c%5E2d%2B9cd)
The first step to factor taking out the GCF is to write each term in prime factored form, so:
![\begin{gathered} 18cd^2=2\times3\times3\times c\times d\times d \\ 12c^2d=2\times2\times3\times c\times c\times d \\ 9cd=3\times3\times c\times d \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2018cd%5E2%3D2%5Ctimes3%5Ctimes3%5Ctimes%20c%5Ctimes%20d%5Ctimes%20d%20%5C%5C%2012c%5E2d%3D2%5Ctimes2%5Ctimes3%5Ctimes%20c%5Ctimes%20c%5Ctimes%20d%20%5C%5C%209cd%3D3%5Ctimes3%5Ctimes%20c%5Ctimes%20d%20%5Cend%7Bgathered%7D)
The second step is to identify the factors common in all terms, they are: 3xcxd
Finally, factor out the GCF:
![3cd(6d+4c+3)](https://tex.z-dn.net/?f=3cd%286d%2B4c%2B3%29)
The answer is above
Answer:
Option: C is correct.
![x=\ln\sqrt{\dfrac{t+1}{1-t}}](https://tex.z-dn.net/?f=x%3D%5Cln%5Csqrt%7B%5Cdfrac%7Bt%2B1%7D%7B1-t%7D%7D)
Step-by-step explanation:
We are asked to solve for 'x' such that we are given a equation as:
![\dfrac{e^x-e^{-x}}{e^x+e^{-x}}=t](https://tex.z-dn.net/?f=%5Cdfrac%7Be%5Ex-e%5E%7B-x%7D%7D%7Be%5Ex%2Be%5E%7B-x%7D%7D%3Dt)
This equation could also be written as:
![e^x-e^{-x}=t(e^x+e^{-x})\\\\e^x-e^{-x}=te^x+te^{-x}\\\\e^x-te^x=te^{-x}+e^{-x}\\\\(1-t)e^x=(t+1)e^{-x}\\\\e^{2x}=\dfrac{t+1}{1-t}](https://tex.z-dn.net/?f=e%5Ex-e%5E%7B-x%7D%3Dt%28e%5Ex%2Be%5E%7B-x%7D%29%5C%5C%5C%5Ce%5Ex-e%5E%7B-x%7D%3Dte%5Ex%2Bte%5E%7B-x%7D%5C%5C%5C%5Ce%5Ex-te%5Ex%3Dte%5E%7B-x%7D%2Be%5E%7B-x%7D%5C%5C%5C%5C%281-t%29e%5Ex%3D%28t%2B1%29e%5E%7B-x%7D%5C%5C%5C%5Ce%5E%7B2x%7D%3D%5Cdfrac%7Bt%2B1%7D%7B1-t%7D)
on taking logarithmic function on both the sides we have:
![2x=\ln (\dfrac{t+1}{1-t})](https://tex.z-dn.net/?f=2x%3D%5Cln%20%28%5Cdfrac%7Bt%2B1%7D%7B1-t%7D%29)
(since
)
as we know ![\dfrac{1}{2}\times \ln b = \ln (b^\frac{1}{2})](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20%5Cln%20b%20%3D%20%5Cln%20%28b%5E%5Cfrac%7B1%7D%7B2%7D%29)
Hence, we have: ![x=\ln\sqrt{\dfrac{t+1}{1-t}}](https://tex.z-dn.net/?f=x%3D%5Cln%5Csqrt%7B%5Cdfrac%7Bt%2B1%7D%7B1-t%7D%7D)
Hence, option C is correct.
Hi Again The Answer Is A Prime Glad To Help! :)
Answer is j(x) everything else i think is incorrect.