Factorisation of 2x2 + 3x + 1 is

The correct answer is Option (2) → (x + 1)(2x + 1)

A quadratic \(ax^2+bx+c\) is factorised by splitting the middle term into two parts whose sum is \(b\) and whose product is \(ac\). Here \(ac=2\times1=2\) and \(b=3\), so the parts are \(2x\) and \(x\).

• Splitting \(3x\) into \(2x+x\): \(2x^2+3x+1=2x^2+2x+x+1\)

• Grouping in pairs: \(2x(x+1)+1(x+1)\)

• Common factor \((x+1)\): \((x+1)(2x+1)\)