IB Maths AA SL 1.9 Binomial theorem

IB Mathematics: analysis and approaches guide, first assessment 2021

Practise binomial expansions, coefficient matching and approximations using integer, fractional and negative powers of expressions.

How this is tested

expand expressions such as (1+x)^4 or (1+5x)^(1/2), keeping terms in ascending powers of x
choose the correct binomial term with nCr, powers of x and k, then equate a coefficient to solve for k
use a suitable x value in a truncated expansion to approximate values such as sqrt(1.2) as a fraction

[Maximum number: 5]

In the expansion of $(\sqrt{x}+k)^{12}$ where $k \in \mathbb{Z}$ , the coefficient of the term in $x^{\frac{3}{2}}$ is -112640 .
Find the value of k.