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1 P.3 POLYNOMIALS Objectives: Operations on polynomials Applications of polynomials ( كثيرات الحدود )

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A polynomial in one variable is an algebraic expression of the form ( معاملات ) ( معامل الحد الاكبر أس ) ( درجة )

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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. A polynomial of two terms is a binomial. A polynomial of three terms is a trinomial. 7xy 2 + 2y 8x 2 + 12xy + 2y 2

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4 Polynomials The constant term is 15. The degree is 3. The leading coefficient is 6. The leading coefficient of a polynomial is the coefficient of the variable with the largest exponent. 6x 3 – 2x 2 + 8x + 15 The constant term is the term without a variable. The degree of a polynomial is the greatest of the degrees of any of its terms. The degree of a term is the sum of the exponents of the variables.

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polynomialtermsdegree Leading coefficient 3y 2 - 5x + 7 21x 5 y + 3x 3 + 2y 2 Terms that have exactly the same variables raised the same powers are called like terms coefficients

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Ex: Perform the following operations: combine like terms Rearrange and group like terms.

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7 Products of Binomials F O I L

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8 Products of Binomials FOIL

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9 Multiplication of Polynomials Ex: (x + 2)(x 2 2x + 3) x3x3 2x 2 3x 4x 2x 2 6 x3x3 x 6

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Special Products Difference of Two Squares Squares of Binomials, or Perfect Squares square of the first twice the product square of the last square of the first

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11 Ex: Perform the indicated operations and simplify

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Cubes of Binomials, or Perfect Cubes Ex: Find the indicated product

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Sum and Difference of Two Cubes Ex: Perform the indicated operations and simplify

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14 You’re shining!

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