The graphing calculator can be a
tremendous help when attempting to multiply or factor algebraic
expressions. There are several approaches you may use
depending upon the known information.
Answers can be
"checked" to see if the
correct factors have been found:
(particularly helpful when dealing with multiple choice
questions)
Check Method 1:
Check factors/answer on the home
screen in equation form.
Factor x^{2}  12x + 36.
OR Find (x  6)^{2}.

 Choose your "favorite" positive
onedigit (for ease) integer value and store the
value in x (do not pick 0 or 1).
For example, to store a 7: 7 STO► x
 Hit ENTER.
 Enter the problem to be factored (or
multiplied) and set "=" to one of the
possible answers (or the answer you want to
check).
The "=" sign is under
2nd MATH (TEST) #1 =.
 Hit ENTER.
 If a 0
appears, this is NOT the correct answer.
If a 1 appears, this IS
the correct answer.



Check Method 2:
Check factors/answer by graphing.
Factor x^{2}  12x + 36.
OR Find (x  6)^{2}.

 Enter the expression into the
Y1= on the
calculator.
 Enter the possible answer response into
Y2=.
 Move to the left of the
Y2= and choose
the open circle. This setting will allow
you to clearly see the animated circle
crossing the screen.
 When the answer is correct, the animated
circle will be "riding" on top of the
original graph.
 Keep checking until the correct answer
is found.
 The only difficult feature of this
method is the occasional need to adjust the
viewing window to see the graph.

The animated bubble does not run along the
original curve. It forms its own graph.
This is not the correct solution.

The animated bubble runs along the
original graph. This is the answer. 

Answers can be "found"
by graphing and finding the zeros of an equation.
Graph Method:
Factors can be found by finding the
zeros of an equation.
Find the factors of x^{2}  3x 
4.


Example 1:
(Multiple choice question)
The factors of x^{2} + 5x +6 are
(1) (x + 1)(x + 6)
(2) (x + 3)(x + 2)
(3) (x + 5)(x + 1)
(4) (x + 6)(x  1)

Method 1:
The "favorite" number stored was 7.
When you hit ENTER and a "1" appears,
you have found the
answer. 
Method
2:
The two graphs do not overlap.
This is not the answer.

The animated bubble overlaps the
original graph. This is the answer.

Example 2:
(Multiple choice question)
The room that is shown in the figure below has a floor space
of 2x^{2} + x  15
square feet. If the width of the room is (x + 3) feet,
what is the length?
(1) (x  3)
(2) (2x  5)
(3) (x  5)
(4) (2x + 5) 
Method 1:
Answers are tested until the correct
answer is found.
OR
Check your answer to be sure
you chose wisely. 
Method 2:
