CAIE A-Level Mathematics 2.1.2 Polynomial division

CAIE A-Level Mathematics 2.1.2 Polynomial division
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise dividing degree 3 and 4 polynomials by linear or quadratic divisors to find quotients, remainders and factors.

How this is tested

  • carry out polynomial division far enough to identify the quotient and remainder
  • compare coefficients in p(x)=(divisor)(quotient)+remainder to find constants
  • use a linear factor result to divide p(x) and complete the factorisation

Question 5(a)

[Maximum number: 3]

The polynomial p(x) is defined by p(x)=9x3+18x2+5x+4\mathrm{p}(x)=9 x^{3}+18 x^{2}+5 x+4.

Find the quotient when p(x) is divided by (3 x+2), and show that the remainder is 6 .