Polynomials: Operations 4.3

4.3 INTRODUCTION TO POLYNOMIALS
a. Evaluate a polynomial for a given value of a variable.
b. Identify the terms of a polynomial.
c. Identify the like terms of a polynomial.
d. Identify the coefficients of a polynomial.
e. Collect the like terms of a polynomial.
f. Arrange a polynomial in descending order, or collect like terms and then arrange in descending order.
g. Identify the degree of each term of a polynomial and the degree of the polynomial.
h. Identify the missing terms of a polynomial.
i. Classify a polynomial as a monomial, binomial, trinomial, or none of these.





Objective a
Evaluate a polynomial for a given value of a variable.

When we replace the variable in a polynomial with a number, the polynomial then represents a number called a value of the polynomial. Finding that number, or value, is called evaluating the polynomial.

Example A



Example B



Example C



Objective b
Identify the terms of a polynomial.

Example D



Objective c
Identify the like terms of a polynomial.

When terms have the same variable and the variable is raised to the same power, we say that they are like terms.

Example E



Objective d
Identify the coefficients of a polynomial.



Objective e
Collect the like terms of a polynomial.

Example G Combine like terms.



Objective f
Arrange a polynomial in descending order, or collect like terms and then arrange in descending order.

Example H



Objective g
Identify the degree of each term of a polynomial and the degree of the polynomial.





Objective h
Identify the missing terms of a polynomial.



Example L



Objective i
Classify a polynomial as a monomial, binomial, trinomial, or none of these.