Factorising quadratics

Factorising Quadratics

Intro to Quadratics

• A quadratic is a type of polynomial that has a degree of 2. The general form of a quadratic is ax² + bx + c.
• Factorising is the process of finding the factors that when multiplied give the original quadratic.
• Factorising is used to simplify problems, solve equations, and graph functions.

Steps to Factorise

• Begin with an equation, in the form of ax² + bx + c = 0.
• Factorising a quadratic involves finding the values of ‘a’, ‘b’, and ‘c’ that will create two binomial brackets.
• These brackets will be of the form (dx + e)(fx + g) = 0.
• The pair of numbers ‘e’ and ‘g’ are factors of ‘c’ and also add or subtract to give ‘b’.
• The values ‘d’ and ‘f’ are factors of ‘a’.

Example of Factorising Quadratic Equations

• Let’s factorise x² - 5x + 6 = 0.
• The factors of 6 that will get us -5 when added together are -2 and -3.
• So, the factorised form is (x - 2)(x - 3) = 0.

Working with Coefficients

• Sometimes the coefficient of x² (the ‘a’ value) will not be 1. In this case, consider the coefficients when looking for factors.
• For instance, to factorise 3x² - 12x + 9 = 0, look for two numbers that multiply to (a*c) = 27 and add to -12.

Checking Work

• A tip to verify if a factorization is correct is to multiply out the brackets and ensure that the original quadratic is returned.
• Consistent practice and different problem sets will help improve skill in factorising quadratics, helping with simplification, solving, and graphing.

Remember, factorising quadratics is a key skill in algebra that underpins many other areas, so it’s essential to grasp for broader Maths understanding.