Factorising Quadratics

• “Factorising Quadratics” involves transforming quadratic expressions into their factored form. A quadratic expression is in the form ax² + bx + c, where a, b, and c are constants.

• The first step in factorising a quadratic expression is to identify the values of a, b, and c in the expression.

• Next, find two numbers that multiply to give ac (the product of a and c), and add to give b, the coefficient of the middle term.

• Once these two numbers are identified, rewrite the middle term of the expression as the sum of the two numbers, and express the quadratic expression in four terms.

• Factorise by grouping. Split the quadratic expression into two groups of two terms each and find the common factors.

• By taking out the common factors, the expression should now be in the form of (mx + n)(px + q), where m, n, p, and q are constants. This is the factorised form.

• Always check if the factorised form is correct by expanding it again. It should return to the original quadratic expression if the factorisation is correct.

• Be aware of the difference between factorising a quadratic with a leading coefficient of 1, where a = 1, and factorising a quadratic with a leading coefficient not equal to 1. Different techniques might be needed.

• The method you use for factorising quadratics will depend on the coefficients a, b, and c. If a = 1, it tends to be simpler than if a ≠ 1.

• Factorising quadratics can help solve quadratic equations, allowing you to find the values of x that satisfy the equation.

• Remember that not all quadratic expressions are able to be factorised using integer values. In such cases, other methods such as completing the square or using the quadratic formula are necessary.

• Quadratic expressions also have special cases, such as perfect squares and difference of squares, that have unique factorising methods. For instance, difference of squares can be factorised into the form (a + b)(a - b).