L03 - Lecture 3 Section A.3 Polynomials and Factoring...

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Unformatted text preview: Lecture 3: Section A.3 Polynomials and Factoring Polynomials Def. A polynomial in u1D465 is an expression of the form u1D44E u1D45B u1D465 u1D45B + u1D44E u1D45B − 1 u1D465 u1D45B − 1 + ⋅⋅⋅ + u1D44E 1 u1D465 + u1D44E where u1D44E u1D45B , ⋅⋅⋅ , u1D44E are real numbers and u1D45B is a nonnegative integer. NOTE: 1) u1D44E u1D45B , ⋅⋅⋅ , u1D44E are the coefficients of each term. If u1D44E u1D45B ∕ = 0, the polynomial has degree u1D45B , and u1D44E u1D45B is called the leading coefficient. 2) Polynomials with one, two, and three terms are called monomials, binomials, and trinomials, respectively. 3) In standard form , a polynomial is written with descending powers of u1D465 . 4) A polynomial with all u1D44E u1D456 = 0 ( u1D456 = 0 , 1 , ⋅⋅⋅ .u1D45B ) is called the zero polynomial . No degree is assigned to the zero polynomial. ex. State whether each is a polynomial. For each polynomial, rewrite it in standard form and find its degree....
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L03 - Lecture 3 Section A.3 Polynomials and Factoring...

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