What is factorization of quadratic expressions?

1 Answer
Oct 28, 2014

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.