Read e-book online A Note on Functions of Lines (1914)(en)(5s) PDF

By Bliss G.A.

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Extra info for A Note on Functions of Lines (1914)(en)(5s)

Sample text

You should be able to work either way, letting the situation dictate the choice. EXAMPLE 2 Adding Polynomials Add: x4 Ϫ 3x3 ϩ x2, SOLUTION Ϫx3 Ϫ 2x2 ϩ 3x, and 3x2 Ϫ 4x Ϫ 5 Add horizontally: (x4 Ϫ 3x3 ϩ x2) ϩ (Ϫx3 Ϫ 2x2 ϩ 3x) ϩ (3x2 Ϫ 4x Ϫ 5) ϭ x4 Ϫ 3x3 ϩ x2 Ϫ x3 Ϫ 2x2 ϩ 3x ϩ 3x2 Ϫ 4x Ϫ 5 ϭ x4 Ϫ 4x3 ϩ 2x2 Ϫ x Ϫ 5 Remove parentheses. Combine like terms. qxd 24 10/12/09 CHAPTER R EXAMPLE 4:35 PM BASIC ALGEBRAIC OPERATIONS 3 Subtracting Polynomials Subtract: SOLUTION MATCHED PROBLEM 3 ZZZ Page 24 4x2 Ϫ 3x ϩ 5 (x2 Ϫ 8) Ϫ (4x2 Ϫ 3x ϩ 5) ϭ x2 Ϫ 8 Ϫ 4x2 ϩ 3x Ϫ 5 ϭ Ϫ3x2 ϩ 3x Ϫ 13 from x2 Ϫ 8 2 Ϫ4x ϩ 3x Ϫ 5 Ϫ3x2 ϩ 3x Ϫ 13 or 2x2 Ϫ 5x ϩ 4 Subtract: x2 Ϫ 8 from d Change signs and add.

A) 218x4y3 9 (B) 2 8x6y3 (C) 30 1 16x 4 (D) 5x3 B y Eliminating a radical from a denominator [as in Example 7(C)] is called rationalizing the denominator. To rationalize the denominator, we multiply the numerator and denominator by a suitable factor that will leave the denominator free of radicals. This factor is called a rationalizing factor. If the denominator is of the form 1a ϩ 1b, then 1a Ϫ 1b is a rationalizing factor because (1a ϩ 1b)(1a Ϫ 1b) ϭ a Ϫ b Similarly, if the denominator is of the form 1a Ϫ 1b, then 1a ϩ 1b is a rationalizing factor.

Polynomials in three or more variables are defined in a similar manner. Polynomials can be classified according to their degree. If a term in a polynomial has only one variable as a factor, then the degree of that term is the power of the variable. If two or more variables are present in a term as factors, then the degree of the term is the sum of the powers of the variables. The degree of a polynomial is the degree of the nonzero term with the highest degree in the polynomial. Any nonzero constant is defined to be a polynomial of degree 0.

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A Note on Functions of Lines (1914)(en)(5s) by Bliss G.A.

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