Factorising quadratics ax^2 + bx + c where a is not 1

Task goals

• Factorise quadratics ax^2+bx+c where a is not 1, with positive coefficients b and c.
• Factorise quadratics ax^2+bx+c where a is not 1, with negative b and/or c.
• Complete a partially factorised quadratic, or identify which of two given factorisations is correct.
• Factorise harder quadratics with larger coefficients, including taking out a common factor first and factorising expressions with a negative leading coefficient.
• Determine whether a given factorisation of a quadratic is correct and explain any error.
• Solve a quadratic equation by factorising and setting each factor equal to zero.
• Find an unknown coefficient in a quadratic given its factorised form, and expand or construct quadratics from given factors.