What Is Factored Form?

By Staff WriterLast Updated Apr 8, 2020 11:59:28 PM ET

Factored form is defined as the simplest algebraic expression in which no common factors remain. Finding the factored form is useful in solving linear equations.

Factored form may be a product of greatest common factors or the difference of squares. For instance, the factored form of x^3 + 2x^2 - 6 = x(x+2)(x-3) and the factored form of x^2 - 16 = (x+4)(x-4)

It is possible to solve for x by using factored form; x^2 + 5x + 6 can be reduced to its factored form by removing the x as a common factor. This results in (x+2)(x+3). Once in the factored form, solve for x by multiplying to get zero. In the equation (x+2)(x+3) = 0, the zero factor property explains that anything multiplied by zero equals zero. This means x + 2 = 0 and x + 3 = 0. The solutions to this formula would be x = -2 and x = -3.

Once the solutions for x are found, check to make sure they work. In the equation x^2 + 5x + 6 = 0, it was found that x = -2, -3. Replace x in the equation with each of the solution values. So, [-2]^2 + 5(-2) + 6 = 0 turns into 4 - 10 + 6 = 0, which is correct, and [-3]^2 + 5(-3) + 6 = 0 becomes 9 - 15 + 6 = 0, which is also correct.