# Something that can have different values at different times. A variable is usually represented by a letter in algebraic expressions.

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1 Lesson Objectives: Students will be able to define, recognize and use the following terms in the context of polynomials: o Constant o Variable o Monomial o Binomial o Trinomial o Polynomial o Numerical coefficient o Term o Linear o Quadratic o Cubic o Quartic o Degree of a term o Degree of a polynomial o Like Terms o Collecting Like Terms Students will be able to recognize certain algebraic expressions as being polynomials Students will be able to classify polynomials based on number of terms or degree Students will be able to simplify polynomials based on like terms Students will be able to evaluate polynomials when provided with values for the variables. Students will be able to simplify polynomials based on like terms. Students will be able to evaluate polynomials when provided with values for the variables. Students will demonstrate the ability to add and/or subtract polynomials by collecting like terms using both a horizontal and vertical format. Students will demonstrate the ability to multiply a monomial monomial, monomial binomial, binomial binomial, and ultimately a general polynomial a general polynomial. Recall the following polynomial vocabulary: Constant: Variable: A quantity that has a fixed value, and does not change. Something that can have different values at different times. A variable is usually represented by a letter in algebraic expressions. Monomial: A Monomial is o a constant, o a variable, or a product of variables o a product of a constant and one or more variables. The Numerical Coefficient is the number (constant) part of a monomial:

2 Example: What are the numerical coefficients of the following monomials: 3 6 5x y 54abc x 0 Polynomial: A Polynomial is an algebraic expression formed by adding or subtracting monomials Note: A polynomial cannot have negative exponents in the variables. Term: Each monomial in the polynomial is called a Term of the polynomial. Classification of Polynomials Polynomials are classified in two different ways:.. Classification Based on Number of Terms: Polynomials that have exactly term are called. Polynomials that have exactly terms are called. Polynomials that have exactly 3 terms are called. Polynomials that have more than three terms are called. Classification based on Degree Definition: Degree of a Term

3 Example: Determine the degree of the following terms x y 54 abc x 0 Definition: Degree of a Polynomial Example: Determine the degree of the following polynomials x 5x 3w + w+ 6 y + 4x y z x z x 0 Polynomials of certain degrees are given special names: Degree Name Example: Complete the following table: 5 4x + x Polynomial + 4x+ 3 + x x 7 4 4x 5x 4 Number of Terms Classification by Number of Terms Degree Classification by Degree 3

4 Simplest Form and Standard Form of a Polynomial Definition: Like Terms Definition: Collecting Like Terms Definition: Simplest Form of a Polynomial Definition: Standard Form of a Polynomial Evaluating Polynomials Example: Evaluate the following polynomials or the specified values of the variables: x + 4x for x = y + 4x y z x z for x=, y=, z = 3 4

5 Polynomial Operations Adding Polynomials Example: Add the following polynomials. Add x + 4x+ 3 to x + 5x+ Add 3 3y 3y y to 5 6y + y Example: Write an expression in simplest form for the perimeter of the figure shown to the right. Determine the perimeter if x = 4 5

6 Subtracting Polynomials Example: Subtract x + 4x+ 3 from x + 5x+ Multiplication of Polynomials Monomial by Monomial Example: Multiply the following: ( 5 m )( mn) ( 5 xy)(4 cxy) ( xyz)( xyz)( xyz) Multiplication of Polynomials Monomial by Polynomial 6

7 Example: Multiply the following: 3 4 x(y+ 8 z) 6( ba + ab 3ab+ 7ab + 0) Multiplication of Polynomials Polynomial by Polynomial Example: Expand the expression 3 (x + x 5)( x + x+ ) 7

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