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Tallahassee Community College

Solving Quadratic Equations by Factoring

In this lab assignment we will be solving equations that are called quadratic equations. A

2

quadratic equation is an equation of the form ax

+ bx + c = 0, where a ≠ 0. A quadratic

equation is in standard form when the polynomial is in descending order and equal to zero.

To solve an equation by factoring we will be using the following principle.

Principle of Zero Products

If

a

⋅ b

0

=

then a = 0 or b = 0

This principle states that if you have a product equal to zero, then at least one of the factors must

equal zero (since ⋅ 0 anything = 0).

Steps for Solving Equations by Factoring

1. Put the equation in standard form. (The polynomial must be in descending order and equal to

zero.)

2. Factor the polynomial

3. Set each factor equal to 0

4. Solve each equation

Example:

Solve: (y + 8)(y – 5) = 0

Question to ask: Is the equation in standard form?

No, but that is because this example has already been factored for us. It is not in descending

order, but it is equal to 0.

*You can tell a polynomial has been factored if it is written as a multiplication problem—a

product of binomials.

(y + 8)(y – 5) is the polynomial in factored form. So at this point we can set each of the two

factors equal to 0.

y

8

0

y

5

0

+

=

−

=

8

8

5

5

−

−

+

+

y

8

y

5

=

−

=

The solutions are −8, and 5. To check, plug in the solutions for y and see if we get a true

statement.

(

8

8

)(

8

) 5

5 (

8

)(

5

) 5

−

+

−

−

+

−

0

(

13

)

13

0

=

⋅

−

=

⋅

0

0

=

=

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Parent category: Education