Solving Quadratic Equation by Factoring

Quadratic equations are a fundamental concept in algebra, and solving them can be achieved through various methods. One of the most common techniques used to solve quadratic equations is factoring. In this article, we will explore how to solve quadratic equations by factoring.

The process of factoring involves expressing a quadratic expression as a product of two binomials. When factored correctly, each factor must equal zero in order for the overall equation to be true. This means that to solve an equation involving a product of polynomials equal to 0, we can let each factor in turn equal 0 to find all possible solutions.

Let's consider an example of a quadratic equation: x^2/3+3*5x-3*18=3*0. To begin, we multiply each term on both sides of the equation by 3, which results in the equation 3*x^2+9*5x-3*54=0.

Next, we look for two numbers whose product is -54 and whose sum is 9, which are the coefficients of the x-term. These numbers are 6 and 9, so we can write the equation as (x+6)(x-9)=0.

Since each factor must equal zero in order for the overall equation to be true, we set each factor equal to 0 and solve for x: x+6=0 and x-9=0. Solving these two equations gives us the solutions x=-6 and x=9.

Not all quadratic equations can be factored using integer coefficients, but this method is a powerful tool for solving many types of quadratics. Additionally, not all quadratics need to be solved by factoring; other techniques such as completing the square or using the quadratic formula are also available.

In conclusion, solving quadratic equations by factoring is an important technique that can be used to solve a wide range of problems. By understanding how to factor quadratic expressions and solve equations involving products of polynomials equal to 0, you will be well on your way to mastering this essential algebraic concept.

Solving quadratic equation by factoring