February/March 2026 Paper 22

2026 · 8 questions · 14 parts · 50 marks

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Context for question 5

The polynomial

p (x)

is defined by

p (x) = a x^{3} + x^{2} + (a + 1) x + 1,

where

a

is a constant. It is given that the remainder is

- 3

when

p (x)

is divided by

(2 x + 1)

5(a)Polynomial Division Factor TheoremEasy2 marks

Find the value of

a

a =

5(b)Polynomial Division Factor TheoremEasy2 marks

Hence, factorise the expression

p (x) + 3

p (x) + 3 =

5(c)Trigonometric Identities EquationsMedium2 marks

Solve the equation

p (\frac{1}{2 + cosec θ}) + 3 = 0

to find the least positive value of

θ

in degrees.

θ =