### Instruction: Find the greatest value of $a$ such that $a^2-10a+21 \le 0$.### Response: I notice that the expression on the left is a quadratic function of $a$, and it is negative or zero when $a$ is between its two roots.
I can find the roots by factoring the expression: $a^2-10a+21 = (a-3)(a-7)$.