If x² + bx + 16 is a perfect square, find b (b > 0).

**The reasoning** A perfect square trinomial has the form (x + a)² = x² + 2ax + a². Notice the pattern: the constant term is the **square of half the coefficient of x**. Here, our constant is 16, so a² = 16, meaning a = 4 (we take positive since b > 0). Now, the middle term must be 2ax = 2(4)(x) = 8x. Therefore, b = **8**. Check: (x + 4)² = x² + 8x + 16 ✓ **Why the wrong options tempt you** - **A) 4**: You might think "√16 = 4, so b = 4" — but you forgot to double it! The formula is 2a, not just a. - **B) 6**: Random guess, maybe averaging 4 and 8? No mathematical basis. - **D) 16**: You took the constant term itself, forgetting the relationship entirely. **Quick takeaway** For x² + bx + c to be a perfect square: find √c, then **double it** to get b. The middle coefficient is always twice the square root of the constant.