In Exercises 1 –2, determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
To calculate: The coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial
Answer to Problem 1RE
Solution:
The degree of the polynomial is 3.
The leading term of the polynomial is
The leading coefficient of the polynomial is
The coefficient of term
The coefficient of term
The coefficient of term
The coefficient of the constant term is
Explanation of Solution
Given:
The polynomial is
Calculation:
Consider each term of the polynomial
Term | Coefficient | Degree |
The coefficient of term
The coefficient of term
The coefficient of term
The coefficient of the constant term is
Since, the greatest degree of the polynomial is 3.
So, the degree of the polynomial is 3.
Since, the leading term is the term of the greatest degree.
So, the leading term of the polynomial is
Since, the leading term is the term of the greatest degree.
So, the leading coefficient of the polynomial is
Want to see more full solutions like this?
Chapter 5 Solutions
Intermediate Algebra for College Students (7th Edition)
- In Exercises 2-6, fill in the blanks. A shortcut for long division of polynomials is ,in which the divisor must be of the form xk.arrow_forwardFind the polynomials connecting the points (0,1), (1,3), and (2,13) by quadratic interpolation.arrow_forwardConsider the polynomial given below. P(x) = (x − 1)(x − 3)(x − 2)(x − 3) what is the leading coefficent and leading term?arrow_forward
- The polynomial 11.5g + 7.55l + 12.5c - 4016 can be used to estimate the weight of an elephant in kilograms, given the girth g of an elephant at the heart, the lenght l of the elephant, and the circumference c of the elephant's foot pad. Estimate the weight of a 3 year old female elephant girth g = 231 length l = 135 and footpad circumference c = 86. From Elementary Algebra: Concepts and Applications 10th Edition - Section 4.7 page 283 problem 15.arrow_forwardDISCOVER: Nested Form of a Polynomial Expand Q toprove that the polynomials P and Q are the same.arrow_forward
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage