Explanation Given Information: The provided polynomial is 3 x 4 + 2 x 3 w 5 − 12 x 2 w + 4 x 2 − 1 . Consider the provided polynomial, 3 x 4 + 2 x 3 w 5 − 12 x 2 w + 4 x 2 − 1 , The + sign separates the terms of polynomial. The provided polynomial can be written as ( 3 x 4 ) + ( 2 x 3 w 5 ) + ( − 12 x 2 w ) + ( 4 x 2 ) + ( − 1 ) . Therefore, the terms of the polynomial 3 x 4 + 2 x 3 w 5 − 12 x 2 w + 4 x 2 − 1 are 3 x 4 , 2 x 3 w 5 , − 12 x 2 w , 4 x 2 , − 1 . The degree of a term is the exponent power of the algebraic expression. The exponent power of algebraic expressions “ x ” and “ w ” in term 3 x 4 is 4 , in term 2 x 3 w 5 is 3 + 5 = 8 , in term − 12 x 2 w is 2 + 1 = 3 , in term 4 x 2 is 2 and in the term − 1 is 0 . Therefore, the degree of the terms 3 x 4 , 2 x 3 w 5 , − 12 x 2 w , 4 x 2 , − 1 is 4 , 8 , 3 , 2 , 0 respectively. The degree of a polynomial is highest degree of its own monomial. The highest degree of the monomial 2 x 3 w 5 in the polynomial 3 x 4 + 2 x 3 w 5 − 12 x 2 w + 4 x 2 − 1 is 8

13th Edition

ISBN: 9780134707365

Author: Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

Publisher: PEARSON

See similar textbooks

Concept explainers

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Videos

Question

Chapter 4.4, Problem 11MCR

To determine

The terms, degree of each term, degree of the polynomial, leading term, leading coefficient and the constant term of the polynomial 3x4+2x3w5−12x2w+4x2−1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.4, Problem 10MCR

Chapter 4.4, Problem 12MCR

Students have asked these similar questions

How long is a guy wire reaching from the top of a 15-foot pole to a point on the ground 9-feet from the pole? Question content area bottom Part 1 The guy wire is exactly feet long. (Type an exact answer, using radicals as needed.) Part 2 The guy wire is approximatelyfeet long. (Round to the nearest thousandth.)

Question 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w k

Consider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]

Chapter 4 Solutions

Intermediate Algebra (13th Edition)

Ch. 4.1 - 1. Identify the terms and the leading term: . Ch. 4.1 - Identify the coefficient of each term and the...Ch. 4.1 - Identify the terms, the degree of each term, and...Ch. 4.1 - 4. Consider the following polynomials. a. b....Ch. 4.1 - a. Arrange in ascending order: 56x2+7x3x4+10x. b....Ch. 4.1 - a. Arrange in ascending powers of y:...Ch. 4.1 - For the polynomial function P(x)=x22x+5 find...Ch. 4.1 - Veterinary Medicine. Refer to the function and the...Ch. 4.1 - Prob. 1SR Ch. 4.1 - Prob. 2SR

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The terms, degree of each term, degree of the polynomial, leading term, leading coefficient and the constant term of the polynomial 3 x 4 + 2 x 3 w 5 − 12 x 2 w + 4 x 2 − 1 .

Solution Summary: The author explains the degree of the polynomial, the leading term, leading coefficient, and the constant term.

Concept explainers

Videos

The terms, degree of each term, degree of the polynomial, leading term, leading coefficient and the constant term of the polynomial 3x4+2x3w5−12x2w+4x2−1.

Want to see the full answer?

Chapter 4 Solutions