Factorise (x^2+x-20).

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

The direct answer is option A: \((x+5)(x-4)\). For an expression of the form \(x^2+bx+c\), find two numbers whose product is \(c=-20\) and whose sum is \(b=1\). The numbers are \(5\) and \(-4\), because \(5\times(-4)=-20\) and \(5+(-4)=1\). Therefore \(x^2+x-20=(x+5)(x-4)\). Option A is correct. Option B uses \(-5\) and \(4\); their product is also \(-20\), but their sum is \(-1\), giving \(x^2-x-20\), not the given expression. Option C has product \(-20\), but \(2+(-10)=-8\), so its middle term is wrong. Option D has product \(-20\), but \(1+(-20)=-19\), so it also gives the wrong middle term. When the constant is negative, the two numbers have opposite signs; choose their signs so their sum has the required sign.