(2x-1)(x+3)=0 Standard Form

3 min read Jun 16, 2024

Solving Quadratic Equations: From Factored Form to Standard Form

This article will guide you through the process of converting a quadratic equation from its factored form to its standard form. We'll use the example of (2x-1)(x+3) = 0 to illustrate the steps.

Understanding Factored Form

The factored form of a quadratic equation represents the equation as the product of two linear expressions. In our example, the factored form is (2x-1)(x+3) = 0. This form is helpful because it directly reveals the solutions to the equation.

Finding the Solutions

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Applying this to our equation:

2x - 1 = 0
x + 3 = 0

Solving these linear equations, we find:

x = 1/2
x = -3

These are the solutions to the quadratic equation in factored form.

Converting to Standard Form

The standard form of a quadratic equation is ax² + bx + c = 0, where 'a', 'b', and 'c' are coefficients. To convert our factored equation to standard form, we need to expand the product:

FOIL Method: We multiply each term in the first binomial by each term in the second binomial.
- (2x-1)(x+3) = 2x(x+3) - 1(x+3)
Distribute: Expand the products:
- 2x² + 6x - x - 3 = 0
Combine Like Terms: Simplify the equation:
- 2x² + 5x - 3 = 0

This is the standard form of the quadratic equation.

Conclusion

We've successfully converted the equation (2x-1)(x+3) = 0 from factored form to standard form. This process involves expanding the product using the FOIL method and then simplifying the resulting expression. The standard form provides a clear view of the coefficients and allows us to apply various methods for solving the quadratic equation.