Question

What is factorization of quadratic expressions?

Answer 1

Factorization of a quadratic expression is the opposite of expansion, and is the process of putting the brackets back into the expression rather than taking them out.

To factorize a quadratic expression of the form `ax^2+bx+c` you must find two numbers that add together to give the first coefficient of `x` and multiply to give the second coefficient of `x`.

An example of this would be the equation `x^2 + 5x + 6`, which factorizes to give the expression `(x+6)(x-1)`

Now, one might expect the solution to include the numbers 2 and 3, as these two numbers both add together to give 5 and multiply to give 6. However, as the signs differ in the factorized equation, then the solution to the equation must be `(x+6)(x-1)`, as `+6 -1` gives `5`, and `6 times 1` yields a solution of 6.

The equation can be checked by multiplying the solutions back into the equation to give the original quadratic of `x^2 + 5x + 6`.