Question 1. The three rational functions listed below each have a different type of…
MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Question 1. The three rational functions listed below each have a different type of denominator.
(i) State whether the given rational function is proper or improper. If it is improper, reduce it to a proper form by performing polynomial division.
(ii) Factor the denominator completely over the real numbers and write an expression that represents the function as a sum of simpler rational terms whose denominators are powers of the factors obtained in part (i). Do not determine the numerical constants at this stage.
(iii) For every denominator that is an irreducible quadratic, give a clear justification for choosing a linear numerator of the form Ax+B rather than a constant numerator.