Factorising quadratics where a ≠ 1: slide and divide

Task goals

• Slide a across to multiply c, turning ax^2+bx+c into the a=1 look-alike x^2+bx+ac, and factorise that look-alike as usual.
• Divide both numbers in the finished a=1 brackets by a, simplify each fraction, and slide any remaining denominator back in front of x to get the final factorisation.
• Apply slide and divide to quadratics with negative b and/or c, keeping track of signs through the slide, factorise, divide and simplify steps.
• Apply slide and divide with only the first (slide) step given, completing the remaining steps unaided.
• Apply slide and divide unaided to quadratics with larger coefficients (a up to 12).
• Check a slide-and-divide factorisation by expanding it back out, and spot and correct a mistake such as forgetting to slide a denominator back in front of x.
• Find an unknown coefficient in a quadratic given its slide-and-divide factorised form, and use slide and divide inside a rectangle-area context.