Factorising Harder Quadratics worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 24 marks Sheet 1

2 marks
Factorise completely \(27x^2 - 192\)
2 marks
\(20v^2 - 21v - 54 = (4v - 9)(gv + h)\)

This is true for all values of \(v\).

(a)
Work out the value of \(g\).

(b)
Work out the value of \(h\).
2 marks
Factorise \(15w^2 + 28w + 12\)
3 marks
Write \(15y^2 - 48y - 48\) as a product of three factors.
3 marks
Solve the equation \(12x^2 - 13x - 35 = 0\) by factorising.
2 marks
Factorise \(75m^2 - 243\) completely.
2 marks
\(25v^2 - 70v + 48 = (5v - 8)(gv + h)\)

This is true for all values of \(v\).

(a)
Calculate the value of \(g\).

(b)
Calculate the value of \(h\).
2 marks
Factorise fully \(18m^2 - 33m + 5\)
3 marks
Write \(15x^2 - 54x - 24\) as a product of three factors.
3 marks
Solve the equation \(8w^2 - 30w + 7 = 0\) by factorising.

Answers

\(3(3x + 8)(3x - 8)\)
(a) \(5\)
(b) \(6\)
\((3w + 2)(5w + 6)\)
\(3(5y + 4)(y - 4)\)
\(x = -\frac{5}{4}\) or \(x = \frac{7}{3}\)
\(3(5m + 9)(5m - 9)\)
(a) \(5\)
(b) \(-6\)
\((3m - 5)(6m - 1)\)
\(3(5x + 2)(x - 4)\)
\(w = \frac{7}{2}\) or \(w = \frac{1}{4}\)