Chapter 3 Summary #8

Chapter 3 covered polynomial functions, multiplicity, synthetic and long division, the rational zero test, approximating zeros, and rational functions. The equation for a polynomial function is: AnX^n + An-1X^n-1 + An-2 + A1X^1 + Ao. A is the coefficient and ^n is the degree. An example of multiplicity is x^2. You would say is as x with a multiplicity of 2. For synthetic division, the first step is to do complete factorization, then list all the zeros. a+bi is a complex number, a-bi is a conjugate, fl them together. The rational zero test us all the factors of the constant (P) / factors of the leading coefficient (S). The first step for approximating zeros is to divide the interval [a,b] in half by finding its midpoint, m=a+b/2. Then, if f(a) and f(m) have opposite signs, then f has a zero in the interval [a,m]. If f(m) and f(b) have opposite signs, then f has a zero in the interval [m,b]. If f(m) = 0, then m is a zero of f. Finally, compute f(m).