A Quadratic Equation in Standard Form
(a, b, and c can have any value, except that a can't be 0.)
To "Factor" (or "Factorise" in the UK) a Quadratic is to:
find what to multiply to get the Quadratic
The factors of x2 + 3x − 4 are:
(x+4) and (x−1)
Why? Well, let us multiply them to see:
|(x+4)(x−1)||= x(x−1) + 4(x−1)|
|= x2 − x + 4x − 4|
|= x2 + 3x − 4|
Multiplying (x+4)(x−1) together is called Expanding.
In fact, Expanding and Factoring are opposites:
Expanding is easy, but Factoring can often be tricky
It is like trying to find out what ingredients
went into a cake to make it so delicious.
It can be hard to figure out!
So let us try an example where we don't know the factors yet:
First check if there any common factors.
But it is not always that easy ...
Guess and Check
Maybe we can guess an answer?
That is not a very good method. So let us try something else.
A Method For Simple Cases
Luckily there is a method that works in simple cases.
With the quadratic equation in this form:
Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b.
Step 2: Rewrite the middle with those numbers:
Step 3: Factor the first two and last two terms separately:
Step 4: If we've done this correctly, our two new terms should have a clearly visible common factor.