# A4e – Factorising quadratics

This is the students’ version of the page. Log in above for the teachers’ version.

Click the tabs for extension tasks…

• Fully factorise $$x^4-1$$
Hover for hint:

1. Expand $$(x+\frac{1}{2})(x+6)$$. Is it possible factorise this expanded expression so that the factors only contain integer coefficients and constants?
2. Expand $$(x+\frac{1}{2})(2x+6)$$. Is it possible factorise this expanded expression so that the factors only contain integer coefficients and constants?

Stan and Ollie are trying to factorise $$x^2-5x+6$$. Stan writes $$(x-2)(x-3)$$. Ollie writes $$(2-x)(3-x)$$. Are either of them correct? If so, who?

### Factorising non-monic quadratic expressions

Click the “New question” to generate a new expression to factorise. Drag down the slider for a step-by-step solution using the grouping method. Note that the applet will occasionally generate an expression that can be factorised easily by a different method (e.g. completing the square) to help you practise those skills. In these cases, the slider is replaced with a simple button to reveal the answer.

Teacher resources

Teachers: log in to access the following:

• Slides in PPTX (with click-to-reveal answers)
• Slides in PDF (one slide per page, suitable for importing into IWB software)
• Worksheet (with space for student work)
• Handout (slides with exercises only; 4 per page for reduced printing)
Links to past exam and UKMT questions