Which rectangle model correctly represents (2x²+x−15)?

Correct answer: (2x−5)(x+3)

The direct answer is A, (2x−5)(x+3). Expand it by multiplying every rectangle cell: (2x)(x)=2x², (2x)(3)=6x, (−5)(x)=−5x, and (−5)(3)=−15. Combining the two middle contributions gives 6x−5x=x, so the total is 2x²+x−15, exactly the target polynomial. In the rectangle model, the signs of the side labels control the signs of the four regions. Option B gives (2x+5)(x−3)=2x²−6x+5x−15=2x²−x−15, so its middle term is negative. Option C gives (x−5)(2x+3)=2x²+3x−10x−15=2x²−7x−15. Option D gives 2x²+13x−15, not the required expression, because its factors produce the wrong middle coefficient. The constant −15 suggests factors −5 and +3, while the leading term 2x² suggests 2x and x. Memory cue: in a rectangle factorisation model, multiply all four cells, including their signs, before combining like terms.