Stitz-Zeager_College_Algebra_e-book

Definition 92 arithmetic and geometric sequences

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Unformatted text preview: ion (x − 1 − 3x A B C D = + + + 2 + 1)(x + 2) x − 1 (x − 1) x+1 x+2 1)2 (x Turning our attention to non-real zeros, we note that the tool of choice to determine the irreducibility of a quadratic ax2 + bx + c is the discriminant, b2 − 4ac. If b2 − 4ac < 0, the quadratic admits a pair of non-real complex conjugate zeros. Even though one irreducible quadratic gives two distinct non-real zeros, we list the terms with denominators involving a given irreducible quadratic only once to avoid duplication in the form of the decomposition. The trick, of course, is factoring the denominator or otherwise finding the zeros and their multiplicities in order to apply Theorem 8.10. 8.6 Partial Fraction Decomposition 525 We recommend that the reader review the techniques set forth in Sections 3.3 and 3.4. Next, we state a theorem that if two polynomials are equal, the corresponding coefficients of the like powers of x are equal. This is the principal by which we shall determine the unknown coefficients in our p...
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