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Pearson Edexcel IAL Mathematics P2.2.1 Simple algebraic division

Practise dividing polynomials by linear factors, using factor and remainder theorems, and linking remainders to unknown constants.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • substitute the root of ax+b to find a remainder or prove a factor of f(x)
  • use algebraic division to express f(x) as divisor × quotient plus remainder
  • combine a factor theorem result with division to fully factorise a cubic

P2.2.1 - Simple algebraic division question 1

[Maximum number: 2]

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

f(z)=4z3+pz2−24z+108\mathrm{f}(z)=4 z^{3}+p z^{2}-24 z+108

where p is a constant.
Given that -3 is a root of the equation f(z)=0

determine the value of p

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