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$10.00 Perfect A+ solution with full explanations even for true/false questions
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$10.00 Polynomials
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Preview: ... and throughout mathematics and science. They are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics, and are used in calculus and numerical analysis to approximate other functions. Polynomials are used to construct polynomial rings, one of the most powerful concepts in algebra and algebraic geometry.<br>FUNCTIONS CAN BE CATEGORIZED, and the simplest type is a polynomial function. We will define it below. We begin with vocabulary.<br>1. When numbers are added or subtracted, they are called terms. This --<br>4x² + 7x 8<br>-- is a sum of three terms. (In algebra, we speak of a "sum," even though a term may be subtracted.)<br>When numbers are multiplied, they are called factors. This --<br>1. (x + 1)(x + 2)(x + 3)<br>-- is a product of three factors.<br>2. A variable is a symbol that takes on values. A value is a number.<br>Thus if x is the variable and has the value 4, then 5x + 1 has the value 21.<br>3. A constant is a symbol that has a single value.<br>Example 1. The symbols '5' and ' ' are constants.<br>The beginning letters of the alphabet a, b, c, etc. are typically used to denote constants, while the letters x, y, z , are typically used to denote variables. For example, if we write<br>y = ax² + bx + c,<br>we mean that a, b, c are constants (i.e. fixed numbers), and that x and y are variables.<br>4. A monomial in x is a single term of the form axn, where a is a <br>real number and n is a whole number.<br>The following are monomials in x:<br>5x3 , 6.3x, 2.<br>We say that the number 2 is a monomial in x, because 2 = 2x0 = 2· 1. <br><br>5. A polynomial in x is a sum of monomials in x.<br>Example 2. 5x3 4x² + 7x 8.<br>The variable of the polynomial, in this case x, is also called the argument of the polynomial. Here is a polynomial with argument t :<br>t ² 5t + 1.<br>When we write a polynomial, t ...
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$10.00 Polynomials
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Preview: ... l, making the expression:<br>x+7-x^2+3x-2, then combine like terms.<br><br>7.The parentheses add nothing to this expression, simply combine like terms.<br><br>8.8x^3+2x^2-12x-3 Sometimes you have to play with these and group them, like (8x^3+2x^2)-(12x+3) and factor the first part. You can factor out a 2x^2 so you'd have 2x^2(4x+1) and then factor the (-12x+3), factor out a 3 so you have 3(4x+1). Now your ex ...
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u6l1Algebra work.zip (9K)
