A tile arrangement x² + 15x + 54 forms a rectangle. Which constant strips make this arrangement possible?

Correct answer: 6 and 9

The direct answer is D: 6 and 9. Suppose the rectangle sides are (x+a) and (x+b). Multiplication gives x²+(a+b)x+ab. To match x²+15x+54, the constants must satisfy a+b=15 and ab=54. The pair 6 and 9 satisfies both conditions: 6+9=15 and 6×9=54. Thus the rectangle is (x+6)(x+9). Option A has product 54 but sum 29, so its middle coefficient is wrong. Option B has sum 15 but product 50, so its constant term is wrong. Option C has product 54 but sum 21, again giving the wrong middle term. Option D is the only pair satisfying both requirements simultaneously. In a tile model, always check the sum for the coefficient of x and the product for the constant tile; checking only one condition can lead to a tempting but incorrect choice.