Factorise the quadratic polynomial $x^2-4x+3$.

Step-by-step solution

1. Write the quadratic in the form $(x-a)(x-b)$ where $a+b$ equals the coefficient of $x$ and $ab$ equals the constant term.
2. The coefficient of $x$ is $-4$, so $a+b=4$ (note the sign).
3. The constant term is $3$, so $ab=3$.
4. Find two numbers whose sum is $4$ and product is $3$ – they are $1$ and $3$.
5. Hence the factors are $(x-1)$ and $(x-3)$, giving the factorised form $(x-1)(x-3)$.

Concept tested: Factorisation of quadratic

Published 4 October 2026 · How this solution was prepared and checked