What factorising means

Factorising a polynomial is the inverse operation of the product: given a polynomial, we rewrite it as a product of simpler factors. It is one of the most important skills in all of algebra and we shall need it to solve equations, simplify algebraic fractions and study inequalities.

In brief — Factorising techniques

1. Collecting a common factor
2. Partial collecting
3. Difference of squares: $A^2-B^2=(A+B)(A-B)$
4. Special trinomial: $x^2+sx+p = (x+a)(x+b)$ with $a+b=s$ and $ab=p$
5. Sum/difference of cubes: $A^3\pm B^3 = (A\pm B)(A^2\mp AB+B^2)$
6. Ruffini’s rule (for polynomials of degree $\ge 3$)

Links

Topics: Algebraic calculus
Concepts: Factorisation
Methods: Ruffini division · Special products · Common factoring · Polynomial factorisation
Skills: Factorising