Moderate -0.3 This is a straightforward binomial expansion problem requiring identification of a specific term using the general term formula, solving for k, then finding another coefficient. It's slightly easier than average as it involves only one unknown constant, basic algebraic manipulation, and standard binomial coefficient calculations with n=4. The two-part structure is routine for this topic.
In the expansion of \(\left(kx+\frac{2}{x}\right)^4\), where \(k\) is a positive constant, the term independent of \(x\) is equal to 150.
Find the value of \(k\) and hence determine the coefficient of \(x^5\) in the expansion. [4]
In the expansion of $\left(kx+\frac{2}{x}\right)^4$, where $k$ is a positive constant, the term independent of $x$ is equal to 150.
Find the value of $k$ and hence determine the coefficient of $x^5$ in the expansion. [4]
\hfill \mbox{\textit{CAIE P1 2024 Q1 [4]}}