CAIE IGCSE Additional Math 3.3 solve cubic equations

Use this cubic-equations page to factor the polynomial first, then solve the remaining quadratic or exact coordinate equation.

Exam points

Use known factors to factorise a cubic polynomial before solving p(x)=0.
Solve the remaining quadratic factor to find all roots of the cubic equation.
Use exact non-calculator algebra when a curve or normal gives a related cubic equation.

[Maximum number: 2]

$p(x)=ax^3+3x^2+bx-12$ has a factor of 2x+1. When p(x) is divided by x-3 the remainder is 105.

Hence solve p(x)=0.

$x=-\frac12$
B1

$x=\pm2$
B1, dep on both B marks in part (b).

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