Moving beyond trial and error to master non-monic quadratics
In short: Factorising quadratics where the x-squared coefficient isn't 1 can be tedious. This video demonstrates a reliable, structured method to break down these complex expressions without relying on endless guesswork.
The video explores a systematic approach to factorising non-monic quadratics, which are equations where the coefficient of the x-squared term is any number other than 1. While trial and error is possible, the presented method involves multiplying the x-squared coefficient by the x-term coefficient and finding factor pairs that sum to the x-term coefficient.
By rewriting the quadratic into a four-term expression, students can group the terms into two parts and factorise each. The goal is to produce two identical brackets. This technique provides a consistent framework for solving non-monic quadratics, which can then be verified by expanding the brackets back to their original form.
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Sources
- Summary by Intellect · source: Factorising Quadratics: Non-Monic | Algebra | Maths | FuseSchool
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