Show that x²+6x+17 can be expressed in the form (x+p)²+q Find the integer values of p and q

The expression is $x^2 + 6x + 17$. The coefficient of $x$ is 6.

Take half of the coefficient of $x$ and square it: $\left(\frac{6}{2}\right)^2 = 3^2 = 9$.
Add and subtract this value to the expression:

The first three terms form a perfect square: $(x+3)^2$.

By comparing $(x+3)^2 + 8$ with $(x+p)^2 + q$, we can identify the values of $p$ and $q$.

The expression is $\boxed{(x+3)^2 + 8}$.
The integer values are $\boxed{p = 3}$ and $\boxed{q = 8}$.