ferrybukantoro
Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

given the polynomial : (3x+4)^5. find the coefficient of x³ !​

Sagot :

Nayefx

Answer:

[tex] \displaystyle 4320 {x }^{3} [/tex]

Step-by-step explanation:

to solve binomials like this there's a way called binomial theorem given by

[tex] \displaystyle {(a + b)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]

but for this question we need the following part

[tex] \displaystyle \boxed{ \binom{n}{k} {a}^{n - k} {b}^{k} }[/tex]

from the question we obtain that a,b and n is 3x,4 and 5 since we want to find the coefficient x³ k should be (5-3) = 2 so we have determined the variables now just substitute

[tex] \displaystyle \binom{5}{2} {(3x)}^{5 - 2} \cdot {4}^{2} [/tex]

simplify which yields:

[tex] \displaystyle \boxed{ \bold{4320 {x }^{3}} }[/tex]

and we are done!

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.