Solving Quadratic Equations by Factoring
Solving an Equation of the Form ax2 + bx + c = 0 by Factoring
The number 0 has several special properties, including this one:
â€¢ The product of 0 and any number is 0. For example, 2 Â· 0 = 0.
Conversely, if the product of two real numbers is 0, then one or both must be 0. This statement is known as the Zero Product Property.
Property â€” Zero Product Property
English If the product of two numbers is 0, then one or both of the numbers is 0.
Algebra If a and b are real numbers, and if a Â· b = 0, then a = 0 or b = 0 or both a and b are equal to 0.
Example If (x + 2)(x + 3) = 0, then x + 2 = 0 or x + 3 = 0.The Zero Product Property is useful for solving certain types of equations.
Solve: (x - 3)(x + 5) = 0
The solutions may be checked by substituting each value of x into the original equation and simplifying.
Definition â€” Quadratic Equation
A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
A quadratic equation written in this form is said to be in standard form.
Notice that the terms on the left side of ax2 + bx + c = 0 are arranged in descending order by degree. The right side of the equation is zero.
Quadratic equations are also called second-degree equations because the degree of the polynomial, ax2 + bx + c, is 2.
We will use the Zero Product Property to solve some quadratic equations by factoring.
Procedure â€” To Solve a Quadratic Equation By Factoring
Step 1 Write the quadratic equation in the form ax2 + bx + c = 0.
Step 2 Factor the polynomial.
Step 3 Use the Zero Product Property.
Step 4 Solve each equation.
Step 5 Check each answer.