Find the product. Simplify your answer. \[ (q+1)(q-4) \]

To find the product of \((q+1)(q-4)\), we can use the distributive property, also known as the FOIL method for binomials. First, multiply the first terms: \(q \cdot q = q^2\). Next, multiply the outer terms: \(q \cdot -4 = -4q\). Then, multiply the inner terms: \(1 \cdot q = q\). Lastly, multiply the last terms: \(1 \cdot -4 = -4\). Now, combine all these results: \[ q^2 - 4q + q - 4 \] Combine like terms \(-4q + q\): \[ q^2 - 3q - 4 \] Thus, the simplified answer is: \[ \boxed{q^2 - 3q - 4} \]