Here is a place you can practise factorising quadratic equations assuming that you have already learnt to do so.
Let's begin with a reminder. Here's a revision video:
Factorising an expression with a constant factor.
Example :: 40h + 88
Identify a common factor of 8 to give \(8(5h+11)\)
Factorising an expression with a variable factor.
Example :: 23h + 3h²
Identify a common factor of h to give \(h(23+3h)\)
Factorising an expression with both a constant and variable factor.
Example :: 10a + 2ab
Identify a common factor of 2a to give \(2a(5+b)\)
Completely factorising an expression of two parts that can be separately factorised.
Example :: 3a + ab + 5w + 4wy
Identify common factors of pairs of terms to give \(a(3+b)+w(5+4y)\)
Writing an expression as the product of two binomials.
Example :: 5a + 5b + ac + bc
Extract common factors of pairs of terms to give \(5(a+b) + c(a+b)\)
Factorising an expression which is the difference between two squares.
Example :: c² - 81
This can be written as \( (c+9)(c-9) \). Expand the brackets to see why
Factorising a quadratic where the squared term coefficient is 1.
Example :: c² - 13c + 36
Start by finding two numbers with a product of 36 and sum of -13
Factorising a quadratic where the squared term coefficient is not 1.
Example :: 4a² + 5a - 6
Multiply the coefficient of a² by the constant term: \( 4 \times -6 = -24 \)
Mixed factorisation questions
Example :: b² + 6b + 9
Use the techniques used in the previous levels
However if you are a teacher would like access to a projectable set of questions to use for whole-class revision click the blue button below:
Factorising quadratic expressions simplifies them by spliting them into simpler parts (factors). It is the reverse of expanding brackets. It is useful in the study of algebraic expressions and graphs and for solving quadratic equations.
Answers are provided for this exercise but they are only available to teachers who have subscribed to Class Admin.
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.