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 - Practice - Page 357: 1

Answer

As shown in the table, the answers for this practice question are in blue ink.
1486088590

Work Step by Step

To find the coefficients of the terms, 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, $-6x^{6}$ + $4x^{5}$ + $7x^{3}$ - $9x^{2}$ - 1, 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 practice problem. So, in the table given, the first term is $7x^{3}$. The corresponding blank in the table is asking for this term's coefficient, which is 7. If we break down this term, we would understand that $7x^{3}$ is a shortened way to write: $x^{3}$ + $x^{3}$ + $x^{3}$ + $x^{3}$ + $x^{3}$ + $x^{3}$ + $x^{3}$. So, if we then ask "How many of each variable is there?", the answer would be 7. The 2nd blank in the table is asking for the term. Since the given coefficient is -9, we know to look for the term in the polynomial that shows -9 of a certain variable. So, the answer is -$9x^{2}$. The third blank in the table is like the first blank of the table, so we know to ask once again, "How many of $x^6$ are there in $-6x^{6}$?" The answer is -6. The 4th blank in the table is like the 2nd blank in the table, which asks for the term. Since the given coefficient is 4, we know to look for the term in the polynomial that shows 4 of a certain variable. So, the answer is $4x^{5}$. The 5th blank in the table provides the term, which is -1, and asks for the coefficient. The coefficient is also -1, because -1 in the equation is known as a Constant. It can also be written as $-1x^{0}$, so, either way, the answer is still -1.
Small 1486088590
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