$solve quadratic equations by factoring$

#Solve quadratic equations by factoring how to

In sharing their solution methods and results with partners, they can expand their understanding by seeing different solutions and correcting their own and their partners’ errors. By attempting solutions individually, students gain an immediate sense of how well they understand the techniques. The think-pair-share activity presents students with representations of all three types of trinomial factoring. Students are able to recognize that the property applies not only to monomials, but also to binomials, and is applicable for all real numbers. In applying it to binomial factors, they can use the property as a tool in a way that has not previously been represented. The Zero Product Property is an elementary concept that is familiar to students. By illustrating these connections, students can see how general solutions are possible. The example of x² + x - 6 shows students the relationship between the zeros of the function, the roots of the equation, and the constant terms of the binomial factors of the trinomial. The lesson includes recognizing and using trinomials in various forms. This lesson helps students to develop skills in solving quadratic equations by factoring and provides them with useful techniques for factoring and for understanding the rationale that supports finding solutions. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.Īctive Engagement, Modeling, Explicit Instruction W:.Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.Patterns exhibit relationships that can be extended, described, and generalized.Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations. Families of functions exhibit properties and behaviors that can be recognized across representations.We want to add 14x to both sides of the equation: 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: 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.

#Solve quadratic equations by factoring how to

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.