College Algebra (5th Edition)
College Algebra (5th Edition)
5th Edition
ISBN: 9780321969576
Author: Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Publisher: PEARSON
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Chapter 4.CT, Problem 1CT

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial as constant, linear, quadratic, cubic, or quartic.

1. f(x)=2x3+6x2x4+11

Expert Solution & Answer
Check Mark
To determine

To find:

The leading term, the leading coefficient, the degree and the type of given polynomial f(x)=2x3+6x2x4+11.

Answer to Problem 1CT

Solution:

The leading term is x4. The leading coefficient is 1. The degree of the polynomial is 4. The type of the polynomial is quartic.

Explanation of Solution

Given:

The given polynomial is f(x)=2x3+6x2x4+11.

Concept:

            (a) The leading term is the first term of a polynomial arranged in descending order of their powers.

            (b) The leading coefficient is the coefficient of leading term.

            (c) The degree is the highest power of a polynomial.

            (d) The type of a polynomial is defined by its degree.

                            1 A polynomial with degree zero is the constant polynomial function.

                            2 A polynomial with degree one is the linear polynomial function.

                            3 A polynomial with degree two is the quadratic polynomial function.

                            4 A polynomial with degree three is the cubic polynomial function.

                            5 A polynomial with degree four is the quartic polynomial function.

The given polynomial f(x) is in descending order,

f(x)=x4+2x3+6x2+11.

The first term of the polynomial is x4. So, the leading term is x4.

The coefficient of the leading term is 1. So, the leading coefficient is 1.

The leading term has the highest power of 4. So, the degree of the polynomial is 4.

The degree of the polynomial is 4. So, the polynomial is a quartic polynomial.

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Chapter 4 Solutions

College Algebra (5th Edition)

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