Find the indicated coefficient or term.
-The coefficient of $x$ in the expansion of $( 3 x + 4 ) ^ { 5 }$
A) 960
B) 3,840
C) 5,120
D) 2,880

Question

Quizplus · Accepted Answer

The coefficient of $x$ in the expansion of $( 3 x + 4 ) ^ { 5 }$ is 3,840. This can be found using the binomial theorem, which states that the coefficient of the $x^k$ term in the expansion of $( a + b ) ^ { n }$ is ${ n \choose k } a ^ { n - k } b ^ { k }$. In this case, $a = 3x$, $b = 4$, $n = 5$, and $k = 1$. So the coefficient of the $x$ term is ${ 5 \choose 1 } ( 3x ) ^ { 5 - 1 } ( 4 ) ^ { 1 } = 5 \cdot 3 ^ { 4 } \cdot 4 = 3,840$.

Find the Indicated Coefficient or Term xxx In the Expansion Of (3x+4)5( 3 x + 4 ) ^ { 5 }(3x+4)5

Find the Indicated Coefficient or Term $x$ In the Expansion Of $( 3 x + 4 ) ^ { 5 }$