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 algebra video tutorial explains how to solve quadratic equations by factoring in addition to using the quadratic formula. 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). 0:00 / 6:22 Solving a quadratic equation by factoring Algebra II Khan Academy Fundraiser Khan Academy 8.17M subscribers Subscribe Subscribed Share 1. 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: 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. You can understand why this is true by looking at some graphs.Over the course of the last few lessons, we have learned to factor quadratic expressions. In the solution to the above exercise, the factor \(4\) does not affect the solutions of the equation at all. We substitute \(64\) for \(h\) in the formula, and solve for \(t\text\) seconds, the ball is \(64\) feet high on its way down. Half-Angle and Angle Sum and Difference Identities.Introduction to Trigonometric Identities.Before approaching this topic, it’s important that you’re able to factor fully. We’ll consider what it actually means graphically to solve a quadratic equation and how this process looks for a variety of equations. Modeling with Generalized Sinusoidal Functions In this video, we’ll learn how to solve quadratic equations by factoring, sometimes called factorizing.Relationships Between Trigonometric Functions.III College Trigonometry 1 Introduction to Trigonometry Short-Run Behavior of Rational Functions.Long-Run Behavior of Rational Functions.Comparing Exponential and Linear Growth.Brief Intro to Composite and Inverse Functions.II College Algebra 1 Functions and Their Graphs Solving Polynomial Equations by Factoring.Factoring Trinomials Using the \(ac\)-method.Applications of Systems of Linear Equations.I Intermediate Algebra 1 Introduction to Intermediate Algebra
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