SPS SPS SM Pure 2024 June — Question 4

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2024
SessionJune
TopicFactor & Remainder Theorem
TypeVerify factor then simplify rational expression

  1. In this question you must show all stages of your working.
Solutions based entirely on calculator technology are not acceptable. $$f ( x ) = 4 x ^ { 3 } - 4 x ^ { 2 } - 7 x - 2$$ a) Use the factor theorem to show that ( \(2 x + 1\) ) is a factor of \(f ( x )\).
b) Write \(\frac { 3 x + 4 } { f ( x ) }\) in partial fraction form.