OCR MEI C1 — Question 11

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
TopicCurve Sketching
TypeTranslation with root finding

11 A cubic polynomial is given by \(\mathrm { f } ( x ) = x ^ { 3 } + x ^ { 2 } - 10 x + 8\).
  1. Show that \(( x - 1 )\) is a factor of \(\mathrm { f } ( x )\). Factorise \(\mathrm { f } ( x )\) fully.
    Sketch the graph of \(y = f ( x )\).
  2. The graph of \(y = \mathrm { f } ( x )\) is translated by \(\binom { - 3 } { 0 }\). Write down an equation for the resulting graph. You need not simplify your answer.
    Find also the intercept on the \(y\)-axis of the resulting graph.