Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.5 The Binomial Theorem - 11.5 Assess Your Understanding - Page 857: 32


The coefficient of the term that contains $x^3$ is: $1760$

Work Step by Step

According to Binomial Theorem, the term containing $x^k$ in the expansion of $(x+p)^n$ can be determined as: $\displaystyle{n}\choose{n-k}$$ p^{n-k}x^k$ Using the above formula and replacing $x$ with $1$ and $p$ with $2$, the term containing $x^3$ in the given expansion can be written as: $\dbinom{12}{12-3}$ $(2)^{3}(1)^{12-3} =\dbinom {12} {9} (2)^{3}(1)^9 \\= \dfrac{12!}{3! \ 9!} (2)^3 \\=220 \times 8\\= 17560$ Therefore, the coefficient of the term that contains $x^3$ is: $1760$
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