AI Tutor
If multiplying out brackets is like unpacking a box, factorising is packing it back up into its neatest, most organized form.
Every algebraic term has a coefficient (the number multiplying the variable, like 33 in 3x3x) and variable parts, and factorising lets us uncover what they all share.
How do you figure out exactly what number or variable belongs on the outside of the brackets?

Finding the Highest Common Factor

To factorise completely, we find the highest common factor (HCF) — the largest value that divides every term with no remainder.
In 12x+1812x + 18, the numbers 1212 and 1818 share common factors of 11, 22, 33, and 66, but 66 is the largest.
Numbers are straightforward, but what happens when the terms share letters with powers?

Factoring Out Variables and Powers

When terms share the same variable, look for the lowest exponent present across all terms — that lowest power is your variable factor.
For 4x3+6x24x^3 + 6x^2, the numerical HCF is 22 and the variable HCF is x2x^2, giving a total HCF of 2x22x^2 to pull outside: 2x2(2x+3)2x^2(2x + 3).