Adding, multiplying and dividing polynomial and rational expressions, factorising polynomials of degree up to 4, and dividing by linear and quadratic polynomials.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
Quadratics were the warm-up. Cubics and quartics need a system — and the system is division. Learn it once and every factorisation question becomes routine.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Move the roots and test values of x with the remainder theorem.
Copy these into your notebook in your own words — that is how they stick.
aₙxⁿ + … + a₀, whole-number powers; degree = highest power.
Factorise, cancel common FACTORS; add with a common denominator; divide by flipping.
Divide leading terms, multiply back, subtract, bring down; repeat until the degree of the remainder is less than the divisor.
For (x − a): bring down, multiply by a, add; the last number is the remainder.
Dividend = divisor × quotient + remainder.
Find one root by trial (factors of the constant term), divide, then factorise the quadratic.
Factorise as two quadratics, or find two roots and divide twice.
Expand your factors or test a value such as x = 0 or x = 1.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (24 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [11 marks]
Let f(x) = 3x³ + 8x² − 20x − 16.
(a) Show that x − 2 is a factor of f(x). [2]
(b) Divide f(x) by x − 2 and hence factorise f(x) completely. [5]
(c) Hence simplify (3x³ + 8x² − 20x − 16)/(3x² + 14x + 8) for x ≠ −4 and x ≠ −2/3. [2]
(d) Solve f(x) = 0. [2]
Question 2 [13 marks]
g(x) = x⁴ + x³ − 7x² − x + 6.
(a) Show that x² − x − 2 divides g(x) exactly and state the quotient. [4]
(b) Hence express g(x) as a product of four linear factors. [3]
(c) Write down the roots of g(x) = 0 in ascending order. [2]
(d) Simplify (x² − 9)/(x² − x − 2) × (x² − 1)/(x² + 2x − 3), stating any values of x for which the expression is not defined. [4]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.