Let $h$ be a polynomial of degree $5$, and suppose that $h(x) = (x^2-7x+10) \cdot g(x)$, where $g(x)$ is a polynomial of degree $b$.  Find $b$.
To find $b$, I need to use the fact that the degree of a product of polynomials is the sum of the degrees of the factors. So, the degree of $h(x)$, which is $5$, must be equal to the degree of $(x^2-7x+10)$ plus the degree of $g(x)$. The degree of $(x^2-7x+10)$ is $2$, since that is the highest power of $x$ in that polynomial. Therefore, $5 = 2 + b$, and solving for $b$, I get $b = 3$. 