Is the equation we will use to demonstrate how to factorise quadratics.
The first step involves using the basic shape of all quadratic factorisation:
We must realize certain equalities that appear between the different expressions of this equation.
This rigid layout can be used to factorise quadratics, but quadratics are all about pattern recognition and a small amount of practice goes a long way.
1. As our quadratic has no number multiplying on x^2 the first step of the solution is simple, we know that both C and D are equal to 1 as 1 only has one factor.
2. This is where paths in the solution diverge, as c in our equation, -6, has a number of factors
Those factors are:
So we know the A and B are one of these factor pairs.
From step 1 in our solution, we know that both C and D are equal to 1. Meaning we can simplify our equation:
Now, from the factors we found in step 2, we must select a pair thats sum equals 1.
+3-2=1, so we know that A=+3 and B=-2 (it is arbritrary which number is assigned to each letter as the rest of the equation is the same).
Finally, checking our answer:
Following a rigid method is not recomended for solving quadratics, remember steps and the equalities that must occur, and practice, are the most important things.