aboutPolynomials - ABOUT POLYNOMIALS A polynomial function in one variable has the form f(x = anxn an-1xn-1 an-2xn-2 a2x2 a1x a0 where n is a whole

aboutPolynomials - ABOUT POLYNOMIALS A polynomial function...

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ABOUT POLYNOMIALS A polynomial function in one variable has the form f(x) = a n x n + a n-1 x n-1 + a n-2 x n-2 + … + a 2 x 2 + a 1 x + a 0 where n is a whole number and a n , a n-1 , a n-2 … a 2 , a 1 , a 0 are real numbers. Polynomial functions can be classified based on the number of terms they have: Monomial functions (one term): f(x) = 2x Binomial functions (two terms): y = –8 + x 2 Trinomial functions (three terms): f(x) = 2x 2 + x - 5 or, based on their degree: First degree ( linear ): f(x) = 2x – 1 Note that y = 1 is also a first degree polynomial. When we determine the degree of a polynomial, we use the highest degree of its terms. Note that the term “y” has degree 1. Second degree ( quadratic ): y = 3x 2 + 2x -2 Third degree ( cubic ): y = x 3 + 1 Fourth degree ( quartic ): f(x) = -2x 4 + 3x 3 – 2x + 1 Fifth degree ( quintic ): f(x) = x 5 + 3 A polynomial can also be classified as an odd-degree or an even-degree polynomial based on its degree. Odd-degree polynomial functions, like y = x 3 , have graphs that extend diagonally across the quadrants. Even-degree polynomial functions, like y = x
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  • Spring '16
  • polynomial function

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