Exercise 1 Page 414

Let's analyze the definitions of degree and a monomial.

• The degree of a polynomial is the highest degree of its monomials.
• A monomial is an algebraic expression with only one term. Monomial expressions involve the multiplication or division of numbers and variables. For instance, 21x^7, 5c^2, and a are monomials.

  Therefore, the first polynomial, c^2+ 2+ c, has three terms: c^2, 2, and c, and its degree is 2. We will analyze all of the given polynomials in the same way.

  	Polynomial	Degree	Number of Terms
  A	- 4x^3	3	1
  B	6y- 3y^5	5	2
  C	c^2+ 2+ c	2	3
  D	- 10d^4+ 7d^2	4	2
  E	- 5z^(11)+ 8z^(12)	12	2
  F	3b^6- 12b^8+ 4b^4	6	3

  Finally, we will order the polynomials by degree from least to greatest.

  Polynomial	Degree	Number of Terms
  c^2+2+c	2	3
  - 4x^3	3	1
  - 10d^4+7d^2	4	2
  6y-3y^5	5	2
  3b^6-12b^8+4b^4	6	3
  - 5z^(11)+8z^(12)	12	2