#Solve a quadratic equation by factoring plus#

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.

#Solve a quadratic equation by factoring plus#

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. In these cases it is usually better to solve by completing the square or using the quadratic formula.An equation containing a second-degree polynomial is called a quadratic equation. However, not all quadratic equations can be factored evenly. Step 4: Set each factor to zero and solve for x.Ģ.2: c = 15, a positive number, therefore both factors will be positive or both factors will be negative.Ģ.3: b = 8, a positive number, therefore the both factors will be positive.Ģ.2: c = -24, a negative number, therefore one factor is negative and the other is positive.Ģ.3: b = 10, a positive number, therefore the larger factor will be positive and the smaller factor negative.įactoring quadratics is generally the easier method for solving quadratic equations. Now that the equation has been factored, solve for x.

If c is negative and b is positive, the larger factor will be positive and the smaller will be negative.Ģ.2: c = -14, a negative number, therefore one factor is negative and the other is positive.Ģ.3: b = 5, a positive number, therefore the larger factor will be positive and the smaller will be negative.Ĭreate two sets of parentheses each containing a x and one of the factors. If c is positive and b is negative, both factors will be negative. If both c and b are negative, the larger factor will be negative and the smaller will be positive.

If both c and b are positive, both factors will be positive. Now create factor pairsĢ.3: Determine the factor pair that will add to give b. If c is negative then one factor will be positive and the other negative. If c is positive then both factors will be positive or both factors will be negative. Step 2: Determine the factor pair of c that will add to give b.įirst ask yourself what are the factors pairs of c, ignoring the negative sign for now. This equation is already in the proper form where a = 1, b = 5 and c = -14.