It has been my experience that students overcomplicate the topic of quadratic equations.
There are a number of different ways to solve quadratic equations in addition to factorising, such as: the ‘difference of two squares’ (Level 6); the quadratic formula (Level 7), plotting the graphs of quadratic functions (Levels 5 – 7) and completing the square (Level 8). However, in this blog I am focusing purely on factorising.
My advice is to get familiar with what a quadratic expression looks like and the steps I have shown below. There are things you need to be familiar with first and they are covered in the next section. Most of the errors I come across are where the student has either missed or got muddled with the rules concerning negative values or made a mistake rearranging the equation.
A quadratic expression is one where the highest power of x in the expressions is x squared (x2). Quadratic equations can be written in the form of:
ax2 + bx + c = 0
where a, b and c are real numbers and a is not equal to zero. This means that the values of a, b and c can be positive as well as negative. They can also be decimals or fractions.
The solutions to a quadratic equation are known as roots and there are generally two to find.
Note: The roots are also the points on a graph where the quadratic curve cuts the x-axis.
How to factorise quadratic equations
Step 1: Rearrange (if necessary)
Make sure the quadratic equation in the form ax2 + bx + c = 0 when factorising.
This may mean you need to rearrange the equation you are given before you start.
This is likely to be the method used in a non-calculator paper
When c = 0, the quadratic will look like this: X2 + bX = 0
Example: X2 – 10X = 0 which will factorise to X(X-10) = 0
Solutions are X=0 and X=10
When b=0 !!!!!
Take care where the coefficient of X2 is greater than 1 (i.e. 3X2) where a is bigger than 1
Example: Factorise 3X2 + 32X = – 20
Step 1: Rearrange to 3X2 + 32X + 20 = 0
Step 2: Prepare brackets. a = 3, b = 32, c = 20 so……….(3X )(X ) = 0
Step 3: Find the values:
j x k = 20 and j + 3k = 32 so………2 x 10 = 20 and 2 + 3×10 = 32
( 3X + 2 )( X + 10 ) = 0
Step 4: Check
( 3X + 2 )( X + 10 ) = 3X2 + 30X + 2X + 20
= 3X2 + 32X + 20
Step 4: Solve
( 3X + 2 ) = 0 , X = -2/3
( X + 10 ) = 0, X = -10
What are the examiners looking for?
Evidence that a correct method has been used – so show your working out!!!
The correct values in the brackets
The final solutions for the two values of X (so don’t forget to state them clearly at the end).
A Bit About Karen
Karen is an experienced, PGCE qualified teacher of Mathematics at Key Stage 3 and above, including the International GCSE. She has been an Examiner and Moderator for Edexcel and therefore has good insight into what examiners are looking for and with exam techniques.
Karen is a skilled creative thinker and problem solver with a passion for identifying untapped talent in individuals so they are able to make a lasting transformational change into the best version of themselves. She provides a safe environment that is non-judgemental, encouraging, positive and challenging, with the freedom to experiment.
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