1140 L3 - Lecture 3: Section A.3 Polynomials and Factoring...

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Lecture 3: Section A.3 Polynomials and Factoring Polynomials Def. A polynomial in x is an expression of the form a n x n + a n ± 1 x n ± 1 + ± ± ± + a 1 x + a 0 where a n ; ± ± ± ; a 0 are real numbers and n is a nonnegative integer. NOTE: 1) a n ; ± ± ± ; a 0 are the coe±cients of each term. If a n 6 = 0, the polynomial has degree n , and a n is called the leading coe±cient. 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 x . 4) A polynomial with all a i = 0 ( i = 0 ; 1 ; ± ± ± :n ) is called the zero polynomial . No degree is assigned to the zero polynomial.
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ex. State whether each is a polynomial. For each polynomial, rewrite it in standard form and ±nd its degree. 1) 0 2) ± 2 3) 2 x 4 ± 1 + 3 x 4) 2 x 5 + 4 x ± p 2 x 5) 5 x ± 7 + p 3 x 8 ± 4 x 5 Operations with Polynomials 1. Addition and Subtracttion of Polynomials: Combine like terms (same variable to the same powers) by adding their coe²cients.
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1140 L3 - Lecture 3: Section A.3 Polynomials and Factoring...

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