What Is Factored Form?
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.