In an area model, \(x^2+9x+18\) can come from which product?

Correct answer: \((x+3)(x+6)\)

The direct answer is B: \((x+3)(x+6)\). Expand it using the area model: \(x\cdot x=x^2\), \(x\cdot6=6x\), \(3\cdot x=3x\), and \(3\cdot6=18\). Adding the four regions gives \(x^2+6x+3x+18=x^2+9x+18\). Thus B produces exactly the required trinomial. A gives \(x^2+7x+2x+14=x^2+9x+14\), so its constant term is wrong. C gives a much larger middle coefficient and constant term. D gives \(x^2+18x+x+18=x^2+19x+18\), so its middle coefficient is wrong. A useful check for \((x+p)(x+q)\) is that \(p+q\) must equal 9 and \(pq\) must equal 18. Only 3 and 6 satisfy both conditions. Memory cue: the side numbers add to the coefficient of x and multiply to the constant term.