Factorising reverses expansion. Remove a common factor first. For x2+bx+c, seek two numbers with sum b and product c. For a non-monic quadratic, check both the outside product and the two cross-products. Example x2-7x+12=(x-3)(x-4), since (-3)+(-4)=-7 and (-3)(-4)=12. 6x2+x-2=(3x+2)(2x-1): its cross-terms are -3x+4x=x. The difference of two squares gives 4x2-25=(2x+5)(2x-5). A common factor must not be left behind: 2x2-18=2(x+3)(x-3). Expand each proposed answer to check its middle term and constant. Factorisation alone does not assign a value to x.

Factorising reverses expansion. Remove a common factor first. For \(x^2+bx+c\), seek two numbers with sum \(b\) and product \(c\). For a non-monic quadratic, check both the outside product and the two cross-products.

\(x^2-7x+12=(x-3)(x-4)\), since \((-3)+(-4)=-7\) and \((-3)(-4)=12\).

\(6x^2+x-2=(3x+2)(2x-1)\): its cross-terms are \(-3x+4x=x\).

The difference of two squares gives \(4x^2-25=(2x+5)(2x-5)\). A common factor must not be left behind: \(2x^2-18=2(x+3)(x-3)\).

Expand each proposed answer to check its middle term and constant. Factorisation alone does not assign a value to \(x\).

Factorising quadratic expressions

Factorising quadratic expressions