If (x+3)(x-5) = x² + bx + c for all values of x, what is the value of b?

Expand using FOIL: $(x+3)(x-5) = x^2 - 5x + 3x - 15 = x^2 - 2x - 15$. Comparing this with $x^2 + bx + c$ gives $b = -2$ and $c = -15$, so the answer is D. Choice A (2) has the right size but the wrong sign; it comes from adding $-5 + 3$ as $+2$ or reading the middle term as $5 - 3$. Choice B ($-15$) is the value of $c$, the constant term, not $b$. Choice C (8) comes from adding $3 + 5$ while ignoring the negative sign on the 5. The middle coefficient is the sum of the two constants, $3 + (-5) = -2$.