Section R4

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Alg 2 Trig Sullivan PPT notes R4

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Sullivan Algebra and Trigonometry: Section R.4Polynomials: 

Sullivan Algebra and Trigonometry: Section R.4 Polynomials Objectives of this Section Recognize Monomials Recognize Polynomials Add, Subtract, and Multiply Polynomials Know Formulas for Special Products

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A monomial in one variable is the product of a constant times a variable raised to a nonnegative integer power. Thus, a monomial is of the form: where a is a constant, x is a variable, and k > 0 is an integer.

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Examples of Monomials

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A polynomial in one variable is an algebraic expression of the form

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Example: Coefficients: 2, 0, -3, 1, -5 Degree: 4

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Polynomials are added and subtracted by combining like terms. Example: Addition

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Example: Subtraction

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Polynomial multiplication can be done by using the distributive property multiple times. Example: Multiplication

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Special Product Formulas Difference of Two Squares Squares of Binomials, or Perfect Squares

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Special Product Formulas Miscellaneous Trinomials Cubes of Binomials, or Perfect Cubes

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Special Product Formulas Difference of Two Cubes Sum of Two Cubes

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Polynomials in Two Variables The degree of a polynomial in two variables is the highest degree of all the monomials with nonzero coefficients. The degree of each monomial is the sum of the powers of the variables.

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