CAIE A-Level Mathematics AS 2.1.2 Polynomial Division Questions

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

Exam points

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

[Maximum number: 3]

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

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

Carry out division at least as far as $3 x^{2}+k_{1} x$
Or equivalent (inspection, ...).

Obtain quotient $3 x^{2}+4 x-1$
Confirm remainder is 6
Answer given - necessary detail needed.

SC B1 for use of the factor theorem to show remainder is 6 if no other marks are awarded.

Alternative Method for Question 5(a)

Synthetic division
-2 / 3 & 9 & 18 & 5 & 4

& & -6 & 8 & -2

& 9 & 12 & -3 & 6
Obtain quotient $3 x^{2}+4 x-1$
Confirm remainder is 6

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CAIE A-Level Mathematics AS 2.1.2 Polynomial Division Questions question 1