Stitz-Zeager_College_Algebra_e-book

# In other words to k0 satisfy denition 91 we need to

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Unformatted text preview: tors and irreducible quadratic factors. Once we have this factorization of the denominator of a rational function, the next theorem tells us the form the decomposition takes. The reader is encouraged to review the Factor Theorem (Theorem 3.6) and its connection to the role of multiplicity to fully appreciate the statement of the following theorem. 3 We will justify this shortly. 524 Systems of Equations and Matrices N (x) is a rational function where the degree of N (x) less than D (x) and N (x) and D(x) have no common factors. Theorem 8.10. Suppose R(x) = the degree of D(x) a • If c is a real zero of D of multiplicity m which corresponds to the linear factor ax + b, the partial fraction decomposition includes Am A1 A2 + ... + + 2 ax + b (ax + b) (ax + b)m for real numbers A1 , A2 , . . . Am . • If c is a non-real zero of D of multiplicity m which corresponds to the irreducible quadratic ax2 + bx + c, the partial fraction decomposition includes B1 x + C1 B 2 x + C2 Bm x + Cm + + ... + 2 + bx + c 2 + bx + c)2 ax (ax2 + bx + c)m (ax for real numbers...
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