AQA Further Paper 1 2023 June — Question 11

Exam BoardAQA
ModuleFurther Paper 1 (Further Paper 1)
Year2023
SessionJune
TopicFactor & Remainder Theorem
TypeSolve inequality involving polynomial

11 The function f is defined by $$f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } - 51 x - 45 \quad ( x \in \mathbb { R } )$$ 11
    1. Fully factorise \(\mathrm { f } ( x )\)
      11
  1. (ii) Hence, solve the inequality \(\mathrm { f } ( x ) < 0\)
    11
  2. The graph of \(y = \mathrm { f } ( x )\) is translated by the vector \(\left[ \begin{array} { l } 7
    0 \end{array} \right]\)
    The new graph is then reflected in the \(x\)-axis, to give the graph of \(y = \mathrm { g } ( x )\)
    Solve the inequality \(\mathrm { g } ( x ) \leq 0\)