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Polynomials and Polynomial Functions
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Definitions

Definitions

5.3 Ц Polynomials and Polynomial Functions

Coefficient: the numerical factor of each term.

Constant: the term without a variable.

Term: a number or a product of a number and variables raised

to a power.

Polynomial: a finite sum of terms of the form axn, where a is a

real number and n is a whole number.

Slide 2

Definitions

Definitions

Monomial: a polynomial with exactly one term.

Binomial: a polynomial with exactly two terms.

Trinomial: a polynomial with exactly three terms.

5.3 Ц Polynomials and Polynomial Functions

Slide 3

Definitions

Definitions

The Degree of a Term with one variable is the exponent on

the variable.

The Degree of a Term with more than one variable is the sum of the exponents on the variables.

The Degree of a Polynomial is the greatest degree of the terms of the polynomial variables.

5.3 Ц Polynomials and Polynomial Functions

Slide 4

Practice Problems

Practice Problems

Identify the degrees of each term and the degree of the polynomial.

5.3 Ц Polynomials and Polynomial Functions

4 𝑎 2 𝑏 4 +3 𝑎 3 𝑏 5 −9 𝑏 4 +4

8

8

4 𝑥 5 𝑦 4 +5 𝑥 4 𝑦 6 −6 𝑥 3 𝑦 3 +2𝑥𝑦

10

10

Slide 5

Practice Problems

Practice Problems

Evaluate each polynomial function

5.3 Ц Polynomials and Polynomial Functions

Slide 6

Multiplication

Multiplication

5.4 Ц Polynomials and Polynomial Functions

Multiplying Monomials by Monomials

Examples:

Slide 7

Multiplying Monomials by Polynomials

Multiplying Monomials by Polynomials

Examples:

5.4 Ц Polynomials and Polynomial Functions

Multiplication

Slide 8

Multiplying Two Polynomials

Multiplying Two Polynomials

Examples:

5.4 Ц Polynomials and Polynomial Functions

Multiplication

Slide 9

Special Products

Special Products

5.4 Ц Multiplying Polynomials

Multiplying Two Binomials using FOIL

First terms

Last terms

Inner terms

Outer terms

Slide 10

Multiplying Two Binomials using FOIL

Multiplying Two Binomials using FOIL

First terms

Last terms

Inner terms

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