Factorise \(x^2+5x\).

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

Correct answer: A. Look for a factor common to both terms. Since \(x^2=x\cdot x\) and \(5x=5 hickspace ext{×} hickspace x\), both terms contain \(x\). Taking it outside leaves one x from the first term and 5 from the second: \(x^2+5x=x(x+5)\). Multiplying back gives \(x hickspace ext{×} hickspace x+x hickspace ext{×} hickspace5=x^2+5x\). B expands to \(5x+5\), so it loses the required \(x^2\) term. C expands to \(x^3+5x\), adding an extra power of x. D expands to \(x^3+5x^2\), also changing both powers. The common-factor rule is: take out the greatest factor shared by every term, then place the quotients inside brackets. Memory cue: after factorisation, distribute the outside factor to check that every original term returns.