Explanation Theorem used: Binomial Theorem “Let x and a be real numbers. For any positive integer n , ( x + a ) n = ( n 0 ) x n + ( n 1 ) a x n − 1 + ( n 2 ) a 2 x n − 2 + ⋯ ( n j ) a j x n − j + ⋯ ( n n ) a n Here, the symbol ( n j ) is said to be a binomial coefficient”. Formula used: “If j and n are integers with 0 ≤ j ≤ n , then ( n j ) = n ! j ! ( n − j ) ! ”. Property used: The property of factorial is n ! = n ( n − 1 ) ! if n ≥ 2 . Calculation: It is given that, g ( x ) = x 5 + 3 and g ( z + 1 ) = ( z + 1 ) 5 + 3 . Compare the given expression ( z + 1 ) 5 with ( x + a ) n , the value of n = 5 and x = z a = 1. Use the Binomial Theorem to expand the binomial ( z + 1 ) 5 as follows. ( z + 1 ) 5 = ( 5 0 ) ( z ) 5 + ( 5 1 ) ( 1 ) ( z ) 4 + ( 5 2 ) ( 1 ) 2 ( z ) 3 + ( 5 3 ) ( 1 ) 3 ( z ) 2 + ( 5 4 ) ( 1 ) 4 ( z ) 1 + ( 5 5 ) ( 1 ) 5 = ( 5 0 ) ( z 5 ) + ( 5 1 ) ( z 4 ) + ( 5 2 ) ( z 3 ) + ( 5 3 ) ( z 2 ) + ( 5 4 ) ( z ) + ( 5 5 ) Apply the above stated formula to find the value of the binomial coefficients as follows

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

See similar textbooks

Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of tw…

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency o…

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow compar…

Videos

Question

Chapter 13.4, Problem 54E

To determine

To find: The expansion of g(z+1) using the Binomial Theorem.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.4, Problem 53E

Chapter 13.4, Problem 55E

Students have asked these similar questions

Find the perimeter and area

Assume {u1, U2, us} spans R³. Select the best statement. A. {U1, U2, us, u4} spans R³ unless u is the zero vector. B. {U1, U2, us, u4} always spans R³. C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set. D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³. OE. {U1, U2, 3, 4} never spans R³. F. none of the above

Assume {u1, U2, 13, 14} spans R³. Select the best statement. A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set. B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector. C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set. D. {U1, U2, us} always spans R³. E. {U1, U2, u3} may, but does not have to, span R³. F. none of the above

Chapter 13 Solutions

Elementary & Intermediate Algebra

Ch. 13.1 - A(n) _____ is a function whose domain is the set...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The expansion of g ( z + 1 ) using the Binomial Theorem.

Solution Summary: The author explains how the expansion of g(z+1) uses the Binomial Theorem.

Concept explainers

Videos

To find: The expansion of g(z+1) using the Binomial Theorem.

Want to see the full answer?

Chapter 13 Solutions