factoring and solving quadratic equations

Factoring and solving quadratic equations how to#
Factoring and solving quadratic equations plus#

For example, expand the factored expression ( x − 2 ) ( x + 3 ) ( x − 2 ) ( x + 3 ) by multiplying the two factors together.Ĭalculate the discriminant b 2 − 4 a c b 2 − 4 a c for each equation and state the expected type of solutions.ī 2 − 4 a c = ( 4 ) 2 − 4 ( 1 ) ( 4 ) = 0. So, in that sense, the operation of multiplication undoes the operation of factoring.

Factoring and solving quadratic equations 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 a ⋅ b = 0, a ⋅ b = 0, then a = 0 a = 0 or b = 0, b = 0, where a and b 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 2 x 2 + 3 x − 1 = 0 2 x 2 + 3 x − 1 = 0 and x 2 − 4 = 0 x 2 − 4 = 0 are quadratic equations. Solving Quadratic Equations by FactoringĪn equation containing a second-degree polynomial is called a quadratic equation.

Factoring and solving quadratic equations how to#

If there is a limited amount of space and we desire the largest monitor possible, how do we decide which one to choose? In this section, we will learn how to solve problems such as this using four different methods.

Proportionally, the monitors appear very similar. The computer monitor on the left in Figure 1 is a 23.6-inch model and the one on the right is a 27-inch model.