Why do you factor quadratic expressions?

Answer 1

You put the quadratic equation in the form polynomial = 0, and then factor the polynomial. A product is zero if one of its factors is zero. Example:

x2 - 5x + 6 = 0

(x-3)(x-2) = 0

x-3 = 0 or x-2 = 0

x = 3 or x = 2

This is a special case of quadratic equations when a is 1. In the above example, c (6) is a small number, then factoring looks simple. However, when c is a big number and contains itself many factors, then factoring becomes complicated and consumes lot of time.

Example 1. Solve: x^2 + 34x - 72 = 0

Example 2. Solve: -x^2 - 26x + 56 = 0

In these cases, the trial and error process to find the correct terms of the two binomials consumes too much time.

There is a new method, called Diagonal Sum Method, that can quickly and directly give the 2 real roots, in these examples, WITHOUT FACTORING.

See Discussion for details.

Answer 2

One of the main reasons this is done is to solve quadratic equations. If you have an equation such as:

x squared + 5x + 6 = 0

(and it is important in this case that the right side be equal to zero), you can solve this through factoring as follows:

(x + 3) (x + 2) = 0

The product can only be equal to zero if one of the factors is zero, so either:

x + 3 = 0

or:

x + 2 = 0

If you solve the two equations separately (which is easy, in this factored form), you get the two solutions (-3, and -2). You can easily check that these are, indeed, solutions to the original equation. Just replace and do the calculations.

Answer 3

Find the expressions which when multiplied give the equation.

eg x2 + 5x + 6 = (x + 2)(x + 3)

Answer 4

A quadratic has nothing to do with finding the factors of a number.