solving a quadratic equation by factoring

SOLVING A QUADRATIC EQUATION BY FACTORING HOW TO
SOLVING A QUADRATIC EQUATION BY FACTORING PLUS

Use grouping to factor and solve the quadratic equation. Set the expressions equal to zero and solve for the variable.ĮXAMPLE 4 Solving a Quadratic Equation Using Grouping Factor out the expression in parentheses.Ħ. The expressions in parentheses must be exactly the same to use grouping.ĥ. Factor the first two terms and then factor the last two terms. Rewrite the equation replacing the term with two terms using the numbers found in step 1 as coefficients of. Find two numbers whose product equals and whose sum equals. With the quadratic in standard form,, multiply. With the equation in standard form, let's review the grouping procedures:ġ. When the leading coefficient is not, we factor a quadratic equation using the method called grouping, which requires four terms. Solving a Quadratic Equation by Factoring when the Leading Coefficient is not

SOLVING A QUADRATIC EQUATION BY FACTORING PLUS

Recognizing that the equation represents the difference of squares, we can write the two factors by taking the square root of each term, using a minus sign as the operator in one factor and a plus sign as the operator in the other. Solve the difference of squares equation using the zero-product property. ĮXAMPLE 3 Using the Zero-Product Property to Solve a Quadratic Equation Written as the Difference of Squares Solve the quadratic equation by factoring. Then, write the factors, set each factor equal to zero, and solve. Solve the quadratic equation by factoring:įind two numbers whose product equals 15 and whose sum equals 8. ĮXAMPLE 2 Solve the Quadratic Equation by Factoring We can see how the solutions relate to the graph in Figure 2. To solve this equation, we use the zero-product property. Note that only one pair of numbers will work. The last pair, sums to, so these are the numbers. Begin by looking at the possible factors of. To factor, we look for two numbers whose product equals and whose sum equals. Solve using the zero-product property by setting each factor equal to zero and solving for the variable.ĮXAMPLE 1 Factoring and Solving a Quadratic with Leading Coefficient of In other words, if the two numbers are and, the factors are. Use those numbers to write two factors of the form or, where is one of the numbers found in step 1.

SOLVING A QUADRATIC EQUATION BY FACTORING HOW TO

HOW TO Given a quadratic equation with the leading coefficient of, factor it.ġ. We have one method of factoring quadratic equations in this form. In the quadratic equation, the leading coefficient, or the coefficient of, is. Solving Quadratics with a Leading Coefficient of 1 Where, and are real numbers, and if, it is in standard form. If then or ,where and are real numbers or algebraic expressions.Ī quadratic equation is an equation containing a second-degree polynomial for example THE ZERO-PRODUCT PROPERTY AND QUADRATIC EQUATIONS We can use the zero-product property to solve quadratic equations in which we first have to factor out the greatest common factor (GCF), and for equations that have special factoring formulas as well, such as the difference of squares, both of which we will see later in this section. We will look at both situations but first, we want to confirm that the equation is written in standard form,, where, and are real numbers, and. The process of factoring a quadratic equation depends on the leading coefficient, whether it is or another integer. If we were to factor the equation, we would get back the factors we multiplied. Set equal to zero, is a quadratic equation. For example, expand the factored expression by multiplying the two factors together. So, in that sense, the operation of multiplication undoes the operation of factoring. Multiplying the factors expands the equation to a string of terms separated by plus or minus signs. In other words, if the product of two numbers or two expressions equals zero, then one of the numbers or one of the expressions must equal zero because zero multiplied by anything equals zero. Solving by factoring depends on the zero-product property, which states that if, then or, where and are real numbers or algebraic expressions. If a quadratic equation can be factored, it is written as a product of linear terms.

Factoring means finding expressions that can be multiplied together to give the expression on one side of the equation. Often the easiest method of solving a quadratic equation is factoring. They are used in countless ways in the fields of engineering, architecture, finance, biological science, and, of course, mathematics. For example, equations such as and are quadratic equations. An equation containing a second-degree polynomial is called a quadratic equation.

Solving a quadratic equation by factoring