To find: Explain why the degree of the product of two nonzero polynomials equals the sum of their degrees.
Answer to Problem 139AYU
The polynomial is saying how many times the variable is multiplied by itself; is, obviously, if you multiply a polynomial by another polynomial, the largest terms in each will be multiplied together and form the new largest term. If you take something times itself a certain number of times and multiply it by the same thing times itself a different number of times, then it just ends up multiplied by itself that many more times;
Highest exponent of product is product of terms of highest degrees, say and .
xxxxx -times
xxxxxx -times
Product has xxxxx xxxxxx times.
Explanation of Solution
The polynomial is saying how many times the variable is multiplied by itself; is, obviously, if you multiply a polynomial by another polynomial, the largest terms in each will be multiplied together and form the new largest term. If you take something times itself a certain number of times and multiply it by the same thing times itself a different number of times, then it just ends up multiplied by itself that many more times;
Highest exponent of product is product of terms of highest degrees, say and .
xxxxx -times
xxxxxx -times
Product has xxxxx xxxxxx times.
Chapter A.3 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Glencoe Math Accelerated, Student Edition
Calculus: Early Transcendentals (2nd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
University Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
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