For how many values of $x$ is the function $y=\frac{x-2}{x^2-7x+10}$ not defined?
The function is not defined when the denominator is zero, because that would make the fraction undefined. So I need to find the zeros of the quadratic equation $x^2-7x+10=0$. To do that, I can try to factor it into two binomials of the form $(x-a)(x-b)$, where $a$ and $b$ are the zeros. I look for two numbers that multiply to $10$ and add to $-7$. I notice that $-2$ and $-5$ work, so I can write $x^2-7x+10=(x-2)(x-5)$. Therefore, the zeros are $x=2$ and $x=5$, and these are the only two values of $x$ that make the function undefined. So the answer is 2. 