Factorising quadratics where a ≠ 1: cross method

Task goals

• Factorise ax^2+bx+c (a not 1, no common factor) using the cross method, with the left column (factor pair of a) already placed in a partly-filled cross.
• Factorise ax^2+bx+c using a fully empty cross (no values given), for quadratics with positive coefficients.
• Factorise quadratics with negative b and/or c using the cross method, choosing the correct signs for the right-hand column.
• Factorise quadratics with larger leading coefficients (up to a=12) using the cross method without any scaffold.
• Diagnose why a particular cross arrangement fails (wrong sum) and find the correct arrangement and factorised form.
• Find an unknown coefficient in a partially given factorised form, or use the cross method in a rectangle-area context to find a missing side length.