AQA C1 2012 June — Question 3

Exam BoardAQA
ModuleC1 (Core Mathematics 1)
Year2012
SessionJune
TopicFactor & Remainder Theorem
TypeKnown polynomial, verify then factorise

3 The polynomial \(\mathrm { p } ( x )\) is given by $$\mathrm { p } ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 5 x - 6$$
    1. Use the Factor Theorem to show that \(x + 1\) is a factor of \(\mathrm { p } ( x )\).
    2. Express \(\mathrm { p } ( x )\) as the product of three linear factors.
  1. Verify that \(\mathrm { p } ( 0 ) > \mathrm { p } ( 1 )\).
  2. Sketch the curve with equation \(y = x ^ { 3 } + 2 x ^ { 2 } - 5 x - 6\), indicating the values where the curve crosses the \(x\)-axis.