Free Algebra
Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

Enter expression, e.g. (x^2-y^2)/(x-y)

Enter expression, e.g. x^2+5x+6

Enter expression, e.g. (x+1)^3

Enter a set of expressions, e.g. ab^2,a^2b

Enter equation to solve, e.g. 2x+3=4

Enter equation to graph, e.g. y=3x^2-1

Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

Solve for:

Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

Math solver on your site

Please use this form if you would like
to have this math solver on your website,
free of charge.

Name:

Email:

Your Website:

Msg:

Solving Equations by Factoring

The Zero Factor Property

The equation ab = 0 indicates that the product of two unknown numbers is 0. But the product of two real numbers is zero only when one or the other of the numbers is 0. So even though we do not know exactly the values of a and b from ab = 0, we do know that a = 0 or b = 0. This idea is called the zero factor property.

Zero Factor Property

The equation ab = 0 is equivalent to the compound equation a = 0 or b = 0.

The next example shows how to use the zero factor property to solve an equation in one variable.

Example 1

Using the zero factor property

Solve x² + x - 12 = 0.

Solution

We factor the left-hand side of the equation to get a product of two factors that are equal to 0. Then we write an equivalent equation using the zero factor property.

	x² + x - 12 = 0
	(x + 4)(x - 3) = 0		Factor the left-hand side.
x + 4 = 0	or	x - 3 = 0	Zero factor property
x = -4	or	x = 3	Solve each part of the compound equation.

Check that both -4 and 3 satisfy x² + x - 12 = 0. If x = -4, we get

(-4)² + (-4) - 12 = 16 - 4 - 12 = 0.

If x = 3, we get

(3)² + 3 - 12 = 9 + 3 - 12 = 0.

So the solution set is {-4, 3}.

The zero factor property is used only in solving polynomial equations that have zero on one side and a polynomial that can be factored on the other side. The polynomials that we factored most often were the quadratic polynomials. The equations that we will solve most often using the zero factor property will be quadratic equations.