Binomial expansion for rational n Quiz

1. What is the coefficient of $x^2$ in the expansion of $(1+x)^{-1}$?

• A. $-1$
• B. $1$
• C. $\frac12$
• D. $2$

2. For which values of $x$ is the expansion of $(3-2x)^{-1}$ valid?

• A. $|x|<\frac32$
• B. $|x|<\frac23$
• C. $|x|<2$
• D. $|x|<3$

3. Find the coefficient of $x$ in the expansion of $\sqrt{1+4x}$.

• A. $1$
• B. $4$
• C. $2$
• D. $\frac12$

4. Which is the correct first step for expanding $(8+x)^{\frac13}$?

• A. $8^{\frac13}(1+x)^{\frac13}$
• B. $8\left(1+\frac{x}{8}\right)^{\frac13}$
• C. $3\left(1+\frac{x}{8}\right)^{\frac13}$
• D. $2\left(1+\frac{x}{8}\right)^{\frac13}$

5. Which value of $x$ may be used in the expansion of $(1+2x)^{-1}$?

• A. $x=1$
• B. $x=-1$
• C. $x=\frac12$
• D. $x=0.1$