# How do you factor x^2-9x+20?

To factorize the quadratic expression ${x}^{2} - 9 x + 20$, one must find the two numbers that add together to give 9, and multiply together to give 20.
Those two numbers are 4 and 5, which factor into the expression $\left(x - 4\right) \left(x - 5\right)$. The signs are due to the fact that the first sign in the expression is a positive, which tells us that both signs must be the same, and the first sign is a negative, which means that, due to the positive sign in the expression, both signs are negative.
To do the opposite, expanding, one must multiply $x$ by $x$, to give ${x}^{2}$, add together $4$ and $5$ to give $9$, and multiply them to give $20$.