![]() For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. In mathematics, this usually means finding the factors of a number. What is Factoring?įactoring is the process of breaking a number or expression down into its component parts. The most common way to solve a quadratic equation is by factoring. If a = 0, then the equation is linear, not quadratic. What is a Quadratic Equation?Ī quadratic equation is an equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are real numbers and x is an unknown. In this blog post, we will explore the box method and the difference between factoring by grouping and factoring by taking out the greatest common factor. There are a few different methods that can be used to factor a quadratic equation. For example, the equation x2 + 5x + 6 can be expressed as (x + 2)(x + 3). The process of solving a quadratic equation by factoring involves expressing the equation as the product of two binomials. A quadratic equation is an equation that contains a term with an exponent of 2, such as x2 + 5x + 6. The process of factoring is often used in solving quadratic equations. For example, the number 12 can be expressed as 2 x 2 x 3, or as 1 x 12. In other words, it’s a way of expressing a number as the product of its factors. In these cases it is usually better to solve by completing the square or using the quadratic formula.Solving Quadratic Equations Using Factoringįactoring is a mathematic process involving the decomposition of a number or algebraic expression into its prime factors. However, not all quadratic equations can be factored evenly. (1,180) (2,90) (3,60) (4,45) (5,36) (6,30) ģ.2: p = -180, a negative number, therefore one factor will be positive and the other negative.ģ.3: b = 24, a positive number, therefore the larger factor will be positive and the smaller will be negative.įactoring quadratics is generally the easier method for solving quadratic equations. Is negative then one factor will be positive and the other negative. This equation is already in the proper form where a = 15, b = 24 and c = -12. Step 1: Write the equation in the general form ax 2 + bx + c = 0. This equation is already in the proper form where a = 4, b = -19 and c = 12.ģ.2: p = 48, a positive number, therefore both factors will be positive or both factors will be negative.ģ.3: b = -19, a negative number, therefore both factors will be negative. Step 8: Set each factor to zero and solve for x. Now that the equation has been factored, solve for x. Using the reverse of the distributive property we can write the outside expressions (shown in red in Step 6) as a second polynomial factor. ![]() ![]() If this does not occur, regroup the terms and try again. Notice that the parenthetical expression is the same for both groups. ![]() Step 7: Rewrite the equation as two polynomial factors. Step 6: Factor the greatest common denominator from each group. Step 4: Rewrite bx as a sum of two x -terms using the factor pair found in Step 3. If p is negative and b is positive, the larger factor will be positive and the smaller will be negative.ģ.2: p = 12, a positive number, therefore both factors will be positive or both factors will be negative.ģ.3: b = 7, a positive number, therefore both factors will be positive. If p is positive and b is negative, both factors will be negative. If both p and b are negative, the larger factor will be negative and the smaller will be positive. If both p and b are positive, both factors will be positive. If p is negative then one factor will be positive and the other negative.ģ.3: Determine the factor pair that will add to give b. If p is positive then both factors will be positive or both factors will be negative. Step 3: Determine the factor pairs of p that will add to b.įirst ask yourself what are the factors pairs of p, ignoring the negative sign for now. c and find the factors of the result, let's call this p.This equation is already in the proper form where a = 3, b = 7 and c = 4. Step 1: Write the equation in the general form
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