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chapter 5 - Chapter5 51:"variablesand exponent"expressions...

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Introduction to Polynomials Chapter 5  
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5-1:Polynomials are sums  of "variables and  exponent" expressions.   Each piece of the polynomial, each part that is  being added, is called a "term ".  Polynomial terms have variables which are raised  to whole-number  exponents (or else the terms  are just plain numbers); there are no square roots  of variables, no fractional powers, and no  variables in the denominator of any fractions.             2x3 + 8x2 – 17x - 3  
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A polynomial is a monomial or a sum of  monomials. A monomial  is an algebraic expression where all  variables are raised to a whole-number power.      5x2,   3x,     8x8y5,    17xy The degree  of a monomial is the sum of the  exponents of the variables.       5x2 has a degree of 2.       3x3y2 has a degree of 5.
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A polynomial is a  binomial  if it contains 2 terms. A polynomial is a  trinomial   if it contains 3 terms. Else, the expression is called a  polynomial. 4 t 5 - 2x 2 2 2 - + x x b a ab b x x 3 2 2 2 2 a 1 2 + - + +
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Coefficient – The number preceding the  variables in a monomial.    In 5x2, the 5 is the coefficient. In the Polynomial 3x2 + 2x – 5 Contains 3 terms 3x2, 2x and -5 3x2 is the leading term-the term with the highest degree. The coefficient 3 is the leading coefficient. The degree of the polynomial is 2 the degree of the  leading coefficient.
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 6 x  –2 This is NOT a polynomial term... ...because the variable  has a negative exponent.  1/ x 2 This is NOT a polynomial term... ...because the variable is  in the denominator.   This is NOT a polynomial term... ...because the variable is  inside a radical.  4 x 2 This IS a polynomial term... ...because it obeys all the  rules. x
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A polynomial or monomial of degree 0 or 1 is  called linear . A polynomial or monomial is said to be  quadratic  if it is of degree 2. A polynomial or monomial is said to be a cubic  if  it is of degree 3.  A polynomial or monomial is said to be a quartic   if it is of degree 4.
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Polynomial Function A polynomial function is a function in which  ordered pairs are determined by evaluating a  polynomial.     Given P(x)= 2x3 + 8x2 – 17x – 3, find the  value of P(2).    P(2)=2(2)3+8(2)2-17(2)-3 =               16 + 32 – 34 -3 = 11                                                  (2,11)
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Addition of Polynomials Polynomials are added by combining like terms.
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