Step 1) Write the quadratic equation in standard form. Either will work as a solution.Įxample 2: Solve each quadratic equation using factoring. Step 3) Use the zero-product property and set each factor with a variable equal to zero: We want to subtract 18 away from each side of the equation: Use the zero-product property and set each factor with a variable equal to zeroĮxample 1: Solve each quadratic equation using factoring.Place the quadratic equation in standard form.In either scenario, the equation would be true:Ġ = 0 Solving a Quadratic Equation using Factoring To do this, we set each factor equal to zero and solve:Įssentially, x could be 2 or x could be -3. This means we can use our zero-product property. The result of this multiplication is zero. In this case, we have a quantity (x - 2) multiplied by another quantity (x + 3). We can apply this to more advanced examples. Y could be 0, x could be a non-zero number X could be 0, y could be a non-zero number The zero product property tells us if the product of two numbers is zero, then at least one of them must be zero: We have four methods for solving quadratic equations: extracting of roots, factoring, completing the square, and using the quadratic formula. This works based on the zero-product property (also known as the zero-factor property). When a quadratic equation is in standard form and the left side can be factored, we can solve the quadratic equation using factoring. For these types of problems, obtaining a solution can be a bit more work than what we have seen so far. Some examples of a quadratic equation are:ĥx 2 + 18x + 9 = 0 Zero-Product Property Up to this point, we have not attempted to solve an equation in which the exponent on a variable was not 1. Generally, we think about a quadratic equation in standard form:Ī ≠ 0 (since we must have a variable squared)Ī, b, and c are any real numbers (a can't be zero) A quadratic equation is an equation that contains a squared variable and no other term with a higher degree. We will expand on this knowledge and learn how to solve a quadratic equation using factoring. A quadratic expression contains a squared variable and no term with a higher degree. Over the course of the last few lessons, we have learned to factor quadratic expressions.
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