What is factored form?

The factored form of a quadratic shows the expression written as two factors multiplied together.

General form:

f(x)=a(x−r1)(x−r2)

Where:

• r1​ and r2 are the zeros (solutions)

Why factored form is useful

Factored form makes it easy to find x-intercepts.

If:

(x−2)(x+3)=0

Then:

• x=2

• x=−3

These are the points where the graph crosses the x-axis.

How to find zeros from factored form

Use the Zero Product Property:

If:

ab=0

Then:

• a=0 or

• b=0

Example

f(x)=(x−1)(x+4)

Set each factor equal to zero:

• x−1=0⇒x=1

• x+4=0⇒x=−4