Which visual rectangle model can factor x² + 18x + 80?

Correct answer: A rectangle with sides (x + 8) and (x + 10)

Direct answer: Option A is correct. To factor x² + 18x + 80 using a rectangle model, find two numbers whose product is 80 and whose sum is 18. The numbers 8 and 10 satisfy both conditions. The four area cells are x·x = x², x·10 = 10x, 8·x = 8x, and 8·10 = 80. Their sum is x² + 10x + 8x + 80 = x² + 18x + 80, so the sides are (x + 8) and (x + 10). Option B has product 80 but sum 24, producing 24x. Option C has product 80 but sum 42. Option D has product 80, but sum 21. Thus each wrong option matches the constant term while failing the middle coefficient. Memory cue: in a monic quadratic, check both the product and the sum, not just the product.