Unformatted text preview: 3. The denominator contains irreducible quadratic factors, none of which are repeated. (We say a quadratic is irreducible if it cannot be factored using real numbers; for example, x 2 +1 is irreducible.) If, say, Q ( x ) = ( ax 2 + p 2 )( bx + q )( cx + r )( dx + s ) ; with ax 2 + p 2 irreducible, then the partial fraction decomposition will be F ( x ) = A 1 x + A 2 ax 2 + p 2 + B bx + q + C cx + r + D dx + s : 4. The denominator contains a repeated irreducible quadratic factor, say Q ( x ) = ( ax 2 + p 2 ) 3 ( bx + q )( cx + r )( dx + s ) : In this case, the partial fraction decomposition takes the form F ( x ) = A 1 x + A 2 ax 2 + p 2 + A 3 x + A 4 ( ax 2 + p 2 ) 2 + A 5 x + A 6 ( ax 2 + p 2 ) 3 + B bx + q + C cx + r + D dx + s :...
View Full Document
- Spring '08
- Fraction, Rational function, Mathematics in medieval Islam