- In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
$$f ( x ) = 4 x ^ { 3 } + a x ^ { 2 } - 29 x + b$$
where \(a\) and \(b\) are constants.
Given that \(( 2 x + 1 )\) is a factor of \(\mathrm { f } ( x )\),
- show that
$$a + 4 b = - 56$$
Given also that when \(\mathrm { f } ( x )\) is divided by \(( x - 2 )\) the remainder is - 25
- find a second simplified equation linking \(a\) and \(b\).
- Hence, using algebra and showing your working,
- find the value of \(a\) and the value of \(b\),
- fully factorise \(\mathrm { f } ( x )\).