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CAIE A-Level Mathematics AS 2.1.3 Factor and Remainder Theorems Questions

Practise evaluating p(a) for factors and remainders, forming simultaneous equations for unknown coefficients and dividing by known linear factors to complete polynomial solutions.

Syllabus
2028–2030
Course
Mathematics 9709
Level
AS

Exam points

  • use vector notation and operations
  • solve geometric problems with vectors
  • interpret vector relationships

CAIE A-Level Mathematics AS 2.1.3 Factor and Remainder Theorems Questions question 1

[Maximum number: 9]

The polynomial p(x) is defined by

p(x)=6x3+ax2+bx−20\mathrm{p}(x)=6 x^{3}+a x^{2}+b x-20

where a and b are constants. It is given that (x+2) is a factor of p(x) and that the remainder is -11 when p(x) is divided by (x+1).

Question (a)

(a)

Find the values of a and b.

[ 5 ]

Question (b)

(b)

Hence factorise p(x), and determine the exact roots of the equation p(3 x)=0.

[ 4 ]
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