Answer
$(x-7)(x-3)$
Work Step by Step
The leading term's coefficient is $1$ so just look for factors of $21$ whose sum is equal to the middle term's coefficient which is $-10$. The factors are $-7$ and $-3$.
Rewrite the middle term ($-10x$) as $-7x-3x$ to obtain:
$x^2-10x+21=x^2-7x-3x+21$
Group first two terms and the group the last two terms together.
$=(x^2-7x)+(-3x+21)$
Factor out the GCF in each group.
$=x(x-7)-3(x-7)$
Factor out $(x-7)$.
$=(x-7)(x-3)$
Hence, the completely factored form of the given expression is $(x-7)(x-3)$.
