January 2022 Repeated Linear Factors Objective To be

January 2022 Repeated Linear Factors Objective: To be able to find partial fractions with repeated linear factors. C 4

Repeated Linear Factors Example Express in partial fractions Let x = 3 Let x = -1 To be able to find partial fractions with repeated linear factors.

Repeated Linear Factors As a first step in putting into partial fractions, check the degree of numerator and denominator. If the degree on numerator ≥ degree on denominator Then divide out first of all. To be able to find partial fractions with repeated linear factors.

Repeated Linear Factors Example Express in partial fractions To be able to find partial fractions with repeated linear factors.

Repeated Linear Factors Example Express in partial fractions Hence (i) Evaluate (ii) Express f(x) as a power series in x as far as the term in x 3 and give the range of convergence in the series. To be able to find partial fractions with repeated linear factors.

Repeated Linear factor in the denominator When occurs in the denominator for partial fractions will arise. The value of P (only) can be found by substituting The value of Q must be found afterwards by substituting any other value of x. Example Express in partial fractions

Repeated Linear Factors Example Express in partial fractions Hence evaluate To be able to find partial fractions with repeated linear factors.