Hints for Solving Quadratics by Factoring
It is imperative that you know how to factor! This is a skill that should have been
mastered in Math 108 or in high school. However, it is understandable that you may be
“rusty” with your factoring techniques. This is why we have several on-line lectures on
factoring.
If you are a student who may need additional help with your factoring, please view the on
line lectures R.1-R.7. Also, you may want to do some problems in the review chapter to fine tune
your skills.
Example: Solve 2 x 2−7 x=−6
The first thing to do when you encounter a quadratic equation is to set the equation equal
2
to 0:
2 x −7 x6=0
Now, there are several techniques that we can use to solve this particular problem. We
can factor, complete the square or use the quadratic formula. Lets factor.
2 x−3 x−2=0
If you do not see how I arrived at the factored step above, YOU MUST WATCH THE
REVIEW ON LINE LECTURES AND LEARN HOW TO FACTOR!
Now looking at the factored equation above you can notice that we have two things
multiplied together which equal 0. This is precisely the “Zero Product Property.”
The Zero Product Property: If ab = 0 then a = 0 or b= 0.
So, using the Zero Product Property we get 2 x−3=0 or x−2=0.
Now solve both equations
2 x=3 or x=2
3
x=
So, our solutions are
or x=2
2
You may see the solution written in “set notation”
{ }
3
,2 .
2