What is the correct factorised form of \(x^2+9x+20\)?

Correct answer: \((x+4)(x+5)\)

The direct answer is B: \((x+4)(x+5)\). For a monic quadratic, choose two numbers whose product is the constant term 20 and whose sum is the coefficient 9. The numbers 4 and 5 work because \(4\times5=20\) and \(4+5=9\). Thus \(x^2+9x+20=(x+4)(x+5)\). Expanding B gives \(x^2+5x+4x+20=x^2+9x+20\). A has product 20 but sum 12, so it gives \(x^2+12x+20\). C has product 20 and sum -9, giving the wrong middle sign. D has product 20 but sum 21, producing \(x^2+21x+20\). The common mistake is checking only the constant term; always check both product and sum. Since both required values are positive, both factors use plus signs.