CAIE A-Level Mathematics 3.1.2 Polynomial Division

CAIE A-Level Mathematics 3.1.2 Polynomial Division
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise dividing cubic or quartic polynomials by linear or quadratic divisors and identifying quotient and remainder through long division, inspection or coefficient comparison.

How this is tested

  • align descending powers and insert zero coefficients before starting polynomial long division
  • subtract each divisor multiple carefully until the remaining degree is below the divisor's
  • state quotient and remainder separately or verify p(x) = divisor × quotient + remainder

Question 4(a)

[Maximum number: 3]

The polynomial p(x) is defined by

p(x)=x4−10x3+20x2−30x+40.\mathrm{p}(x)=x^{4}-10 x^{3}+20 x^{2}-30 x+40 .

Find the quotient when p(x) is divided by (x2+3)\left(x^{2}+3\right) and show that the remainder is -11.