Find the coefficient of the given term in the binomial expansion.
-$x ^ { 4 }$ term, $( x - 2 ) ^ { 11 }$
A) 253,440
B) 42,240
C) $- 253,440$
D) $- 42,240$

Question

Quizplus · Accepted Answer

The binomial expansion of $(x - 2)^{11}$ is given by $\sum_{k=0}^{11} \binom{11}{k} x^{11-k} (-2)^k$. For the $x^4$ term, we need $11-k=4$, so $k=7$. The coefficient is $\binom{11}{7}(-2)^7 = 330 \times (-128) = -42,240$.

Find the Coefficient of the Given Term in the Binomial x4x ^ { 4 }x4

Find the Coefficient of the Given Term in the Binomial $x ^ { 4 }$