Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.3 - Introduction to Polynomials - Exercise Set: 1


The answers for finding the polynomial's terms and coefficients are listed in the table (in blue ink). (The polynomial is $x^{2} - 3x + 5$)

Work Step by Step

To find the coefficients of the terms in the polynomial, $x^{2} - 3x + 5$, it may be easier to ask "How many of each variable is there?" So, to find the coefficients of each term in the given polynomial, we need to look at the numbers in front of the variables given in the terms. But also remember to not look at the exponents, since we are only trying to find the coefficients of the variables in this problem. So, in the table given, the first term is $x^{2}$. The corresponding blank in the table is asking for this term's coefficient. So, if we then ask "How many of "x" is there?", the answer is 1. The 2nd blank in the table is asking for the term. Since the given coefficient is -3, we know to look for the term in the polynomial that shows -3 of a certain variable. So, again we can follow this line of questioning: "How many of each variable is there?" Based on this, we would then recognize that the polynomial's 2nd term, $-3x$, is the correct answer. Remember that it is just a shortened version of $-x -x -x$, which can also be written as $-x + -x + -x$. As such, the answer for the 2nd blank in the table is $-3x$. The third blank in the table is like the first blank, asking for the term's coefficient. However, since the term "$5$" is a constant (which means it is a number that can't be modified by another variable in the polynomial), its coefficient is also "$5$."
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