1. Introduction to Polynomials
5.2
Introduction to Polynomials
1. Identify monomials.
2. Identify the coefficient and degree of a monomial.
3. Classify polynomials.
4. Identify the degree of a polynomial.
5. Evaluate polynomials.
6. Write polynomials in descending order of degree.
7. Combine like terms.
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2. Objective 1
Identify monomials.

3. x, y
a number
Monomial: An expression that is a constant, a variable, or a product of a constant and variable(s) that are raised to whole number powers.
Multiply a number and a variable
Exponent can’t be negative!
Exponent can’t have fractions!

4. Is the given expression a monomial:
Yes
Yes
When an equation in one variable is solved the answer is a point on a line. No No

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Objective 2
Identify the coefficient and degree of a monomial.
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Coefficient of a monomial: The numerical factor in a monomial.
Degree of a monomial: The sum of the exponents of all variables in a monomial.
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7. Identify the coefficient and degree of each monomial:
When an equation in one variable is solved the answer is a point on a line.
C: 16
D: 0
C: 23 = 8
D: 5

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Objective 3
Classify polynomials.
Objective 4
Identify the degree of a polynomial.
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Polynomial: A monomial or an expression that can be written as a sum of monomials.
Examples: 4x, 4x + 8, 2x2 - 5xy + 8y
Polynomial in one variable: A polynomial in which every variable term has the same variable.
Example: x2 – 5x + 2
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Binomial: A polynomial containing two terms.
Trinomial: A polynomial containing three terms.
Degree of a polynomial: The greatest degree of any of the terms in the polynomial.
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11. Identify the type of polynomial and the degree:
Binomial
D: 2
Monomial
D: 3
When an equation in one variable is solved the answer is a point on a line.
Trinomial
D: 3
Polynomial
D: 3
Polynomial
D: 4
Not a polynomial

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Objective 5
Evaluate polynomials.
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13. Evaluate each of the following:
-2(-1)2(4) = -8
(-4)2 – (-4) – 3 = – 3 = 17
- (-1)2 (2) = - (1)(2) = -2

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Objective 6
Write polynomials in descending order of degree.
Objective 7
Combine like terms.
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Writing a Polynomial in Descending Order of Degree
Place the highest degree term first, then the next highest degree, and so on.
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16. Write the polynomial in descending order.

17. Combine like terms and write the resulting polynomial in descending order of degree.

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Classify the expression
a) Monomial
b) Binomial
c) Trinomial
d) None of these
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5.2

19. Copyright © 2011 Pearson Education, Inc.
Classify the expression
a) Monomial
b) Binomial
c) Trinomial
d) None of these
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5.2

20. Copyright © 2011 Pearson Education, Inc.
Evaluate when x = –3.
a) –118
b) –10
c) 10
d) 134
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5.2

21. Copyright © 2011 Pearson Education, Inc.
Evaluate when x = –3.
a) –118
b) –10
c) 10
d) 134
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5.2

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Identify the degree of the polynomial.
a) 3
b) 5
c) 6
d) 7
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5.2

23. Copyright © 2011 Pearson Education, Inc.
Identify the degree of the polynomial.
a) 3
b) 5
c) 6
d) 7
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5.2