For a rational function whose denominator factors completely into distinct linear factors

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

For a rational function

R(x)=\dfrac{P(x)}{Q(x)}

whose denominator

Q(x)

factors completely into distinct linear factors, which of the following additional conditions must be satisfied to express

R(x)

uniquely as the sum of a polynomial and terms of the form

\dfrac{A}{x-r}

? (a)

\deg P(x)=\deg Q(x)

. (b) The remainder obtained when

P(x)

is divided by

Q(x)

has degree less than

\deg Q(x)

. (c)

P(x)

and

Q(x)

share a non-trivial common factor. (d) The leading coefficient of

Q(x)

equals

1