1. The problem is to simplify the expression $16x^2 + 4x + 36$. 2. We look for common factors in all terms. The terms are $16x^2$, $4x$, and $36$. 3. The greatest common factor (GCF) of $16$, $4$, and $36$ is $4$. 4. Factor out the $4$: $$16x^2 + 4x + 36 = 4(\cancel{4} \times 4x^2 + \cancel{4} \times x + \cancel{4} \times 9) = 4(4x^2 + x + 9)$$ 5. The quadratic inside the parentheses, $4x^2 + x + 9$, does not factor nicely with integer factors, so this is the simplified form. Final answer: $$4(4x^2 + x + 9)$$