CAIE A-Level Mathematics 2.1.2 Polynomial division

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

Exam points

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

[Maximum number: 3]

Find the quotient when $x^{4}-32 x+55$ is divided by $(x-2)^{2}$ and show that the remainder is 7 .

Carry out division at least as far as $x^{2}+k x$ or equivalent ...
M1
OE, e.g. comparing coefficients with coefficient of $x^{2}$ equal to 1
and attempt at a second coefficient.
Obtain quotient $x^{2}+4 x+12$
A1
Confirm remainder is 7
A1
AG

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2.1.2—Polynomial division question 1