Section 11 5 Partial Fraction Decomposition Copyright 2013

Section 11. 5 Partial Fraction Decomposition Copyright © 2013 Pearson Education, Inc. All rights reserved

Objectives • Decompose P/Q where Q has only non-repeated linear factors. • Decompose P/Q where Q has repeated linear factors. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Rational expression (P/Q): ratio of two polynomials. • Proper: degree of P < degree of Q If improper, use long division to rewrite as a polynomial and a proper rational term. We are only going to discuss proper rational expressions. Copyright © 2013 Pearson Education, Inc. All rights reserved

Every polynomial with real coefficients can be factored into linear and/or irreducible quadratic factors. The denominator of the rational expression P/Q can only contain • linear factors (x-a) and • irreducible quadratic factors (ax 2+bx+c). (b 2 – 4 ac must be negative if the factor is irreducible. ) Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Choose “convenient” values of x like 2 and -3 Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

No more “convenient” values, so pick something easy. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Ex 4: Ex 5: You will do these in calculus, but we won’t solve them now. Copyright © 2013 Pearson Education, Inc. All rights reserved

Homework: 11. 5: #5 -13 odd, 17, 19 #15, 21, 35 (set up only) Copyright © 2013 Pearson Education, Inc. All rights reserved