How Do You Solve a Quadratic Equation by Factoring?

How Do You Solve a Quadratic Equation by Factoring?

Note:

One of the many ways you can solve a quadratic equation is by factoring it. In this tutorial, you'll see how to factor a quadratic equation using the guess and check method of factoring. Then, use the zero product property to find the solution!

Keywords:

  • problem
  • skill
  • quadratic equation
  • factoring
  • factor
  • zeros
  • zero product property
  • quadratic

Background Tutorials

  • Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

  • Factor a quadratic expression to reveal the zeros of the function it defines.

      • What's the Zero Product Property?What's the Zero Product Property?

      What's the Zero Product Property?

      The zero-product property let's you split the product of factors into separate equations. Then, you can solve each equation to get the solutions to your original equation! Learn all about this very useful property by watching this tutorial.

      • How Do You Factor a Polynomial by Guessing and Checking?How Do You Factor a Polynomial by Guessing and Checking?

      How Do You Factor a Polynomial by Guessing and Checking?

      Factoring trinomials can by tricky, but this tutorial can help! Follow along as a trinomial is factored using the guess and check method. What, no possibilities work? The trinomial must be prime! Watch this tutorial and see what happens!

      • How Do You Figure Out a Template for Factoring a Trinomial?How Do You Figure Out a Template for Factoring a Trinomial?

      How Do You Figure Out a Template for Factoring a Trinomial?

      Did you know that when you're factoring a trinomial, the signs in the trinomial determine the signs in the product of the binomials? This information is really useful when you're factoring trinomials! Watch this tutorial and learn the different sign cases.

  • Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

      • What is a Polynomial?What is a Polynomial?

      What is a Polynomial?

      If you learn about algebra, then you'll see polynomials everywhere! In this tutorial, you'll learn the definition of a polynomial and see some of the common names for certain polynomials.

Further Exploration

  • Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.