Answer
$(x-3)(x-7)$
Work Step by Step
To factor the second-degree polynomial $x^2 - 10x + 21$, we have to find integers whose product is $21$ and whose sum is $-10$. That is, we have $-3$ and $-7$ where $-3-7=-10$ and $-3\times (-7)=21$. Thus
$$
x^2 - 10x + 21=(x-3)(x-7)
.$$