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Ch. 3 - Polynomial and Rational Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 3 - Polynomial and Rational FunctionsProblem 1
Chapter 4, Problem 1

Fill in the blank(s) to correctly complete each sentence. A polynomial function with leading term 3x5 has degree ____.

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1
Recall that the degree of a polynomial function is the highest power of the variable in the polynomial.
Identify the leading term of the polynomial, which is the term with the highest exponent on the variable.
In this problem, the leading term is given as \$3x^{5}$, where the exponent on $x$ is 5.
Therefore, the degree of the polynomial function is the exponent of the leading term, which is 5.
Fill in the blank with the number 5 to complete the sentence: "A polynomial function with leading term \$3x^{5}$ has degree 5."

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Polynomial Function

A polynomial function is an expression consisting of variables and coefficients combined using only addition, subtraction, multiplication, and non-negative integer exponents. For example, 3x^5 + 2x^3 - 7 is a polynomial function.
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Introduction to Polynomial Functions

Leading Term

The leading term of a polynomial is the term with the highest power of the variable, which determines the polynomial's end behavior. In 3x^5 + 2x^3, the leading term is 3x^5.
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End Behavior of Polynomial Functions

Degree of a Polynomial

The degree of a polynomial is the highest exponent of the variable in the polynomial. It indicates the polynomial's overall degree and influences its graph's shape. For example, the degree of 3x^5 is 5.
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Standard Form of Polynomials
Related Practice
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Graph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing. ƒ(x)=-3x2-12x-1

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Fill in the blank(s) to correctly complete each sentence. The highest point on the graph of a parabola that opens down is the ____ of the parabola.

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Textbook Question

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