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Pji*>FACTORING A NUMBER IS THE PROCESS OF FINDING TWO OR MORE 
@EXPRESSIONS THAT WHEN MULTIPLIED EQUAL THE ORIGINAL NUMBER.

.PLEASE PRESS THE LETTER C KEY TO CONTINUE.
C
.PLEASE PRESS THE LETTER C KEY TO CONTINUE.
 AN EXAMPLE OF FACTORING IS*

@THE FACTORS OF 10 ARE 5 AND 2, SINCE 5*2=10 (WHERE 10 IS THE
0ORIGINAL NUMBER , 5 AND 2 ARE THE FACTORS).

(PRESS THE LETTER C KEY TO CONTINUE.
C
.PLEASE PRESS THE LETTER C KEY TO CONTINUE.
>THE FACTORS OF 4X+2 ARE 2 AND (2X+1).  WE ARRIVE AT THESE
@BY NOTING THAT 2 IS THE GREATEST COMMON FACTOR OF 4X AND 2.

DTHIS MEANS THAT THE GREATEST COMMON FACTOR OF BOTH TERMS OF THE
FEXPRESSION IS THE NUMBER THAT MULTIPLIES THE REST OF THE QUANTITY.
0THE QUANTITY IS LOCATED INSIDE OF THE ().  

.PLEASE PRESS THE LETTER C KEY TO CONTINUE.
C
*PLEASE PRESS THE LETTER C TO CONTINUE.
$LET ME GIVE YOU ANOTHER EXAMPLE.

(THE EXPRESSION 9X+3 CAN BE FACTORED.

$     9X CAN BE WRITTEN AS  3X*3.

"     3 CAN BE WRITTEN AS 1*3.

<NOTICE THAT 3 IS COMMON TO BOTH AND IT HAPPENS TO BE THE
@LARGEST COMMON FACTOR OF BOTH.  THIS 3 IS THEN FACTORED OUT
<OF THE 9X AND THE 3.  THE REMAINING FACTORS OF 3X AND 1
WILL BE LEFT IN () SIGNS. 

6THIS GIVES YOU THE FINISHED ANSWER OF*   3(3X+1).

<ALL THE REMAINING FACTORS MUST REMAIN IN THE ().  IT IS
*VERY IMPORTANT FOR THE 1 TO BE THERE.

$PRESS THE LETTER C TO CONTINUE.
C
>NOW LET ME GIVE YOU SOME PROBLEMS TO SEE HOW WELL YOU HAVE
<PICKED UP THE IDEA.  REMEMBER TO FACTOR OUT THE GREATEST
>COMMON FACTOR FIRST AND LEAVE THE SECOND FACTOR IN THE ().
              GOOD LUCK.

$PRESS THE LETTER C TO CONTINUE.
C
FACTOR  8A+6  COMPLETELY.
2(4A+3)

GOOD.
<REMEMBER TO FACTOR OUT THE GREATEST COMMON FACTOR FIRST.
:IN THIS CASE IT IS A 2, WHICH GOES IN FRONT OF THE ().
$THE CORRECT ANSWER IS  2(4A+3).
FACTOR  9A+3B  COMPLETELY.
3(3A+B)
$CORRECT!!! YOU ARE DOING BETTER.
	@THE CORRECT ANSWER IS 3(3A+B) WHERE 3 IS TH GREATEST COMMON
FACTOR.

FACTOR COMPLETELY  2X+6.

2(X+3)

RIGHT.

,I THINK WE WILL DO A LITTLE MORE REVIEW.
FACTOR COMPLETELY  4A-4.

4(A-1)
YOU ARE REALLY DOING FINE.
>THE CORRECT ANSWER IS 4(A-1).  REMEMBER THAT THE 1 MUST BE
@INCLUDED BECAUSE 4 AND 1 ARE THE FACTORS TO BE MULTIPLIED TO
EQUAL 4.
FACTOR  7X+14  COMPLETELY.

7(X+2)

GOOD.
:THE CORRECT ANSWER IS 7(X+2) WHERE 7 IS THE GREATEST 
0COMMON FACTOR.  YOU DO NEED A LITTLE REVIEW.
FACTOR COMPLETELY  6X+8.
2(3X+4)
@SUPER, YOU HAVE DONE A GREAT JOB AND YOU HAVE COMPLETED THIS
:SECTION.  YOU ARE NOW READY TO GO TO THE NEXT SECTION.
FRIE05>THE CORRECT ANSWER IS 2(3X+4) WHERE THE 2 IS THE GREATEST 
COMMON FACTOR.
FACTOR COMPLETELY  9X+12.
3(3X+4)
 GOOD, THAT'S THE RIGHT IDEA.
(YOU COULD USE A LITTLE MORE REVIEW.
FACTOR  6X+15  COMPLETELY.
3(2X+5)
4GOOD SHOW.  NOW LET'S MOVE TO SOMETHING A LITTLE
MORE CHALLENGING.
FRIE05@THE CORRECT ANSWER IS 3(2X+5).  LET'S REVIEW HOW TO FACTOR A
LITTLE MORE.
<LET'S TRY GOING THROUGH THE PROCESS OF FACTORING STEP BY
STEP.  

$PRESS THE LETTER C TO CONTINUE.
C
FRIE04*PLEASE PRESS THE LETTER C TO CONTINUE.
:WHEN WE FACTOR AN EXPRESSION WE MUST FIND THE GREATEST
$COMMON FACTOR OF ALL THE TERMS.
@THE GREATEST COMMON FACTOR IS THE LARGEST NUMBER THAT CAN BE
4DIVIDED EVENLY INTO EACH TERM OF THE EXPRESSION.

$PRESS THE LETTER C TO CONTINUE.
C
*IF WE LOOK AT THE NUMBERS 12, AND 16:

B12 AND 16 CAN BOTH BE DIVIDED EVENLY BY 1,2,4.  THESE ARE THE
@FACTORS THEY HAVE IN COMMON.  4 IS THE LARGEST OF THE COMMON
:FACTORS AND THIS IS CALLED THE GREATEST COMMON FACTOR.

$PRESS THE LETTER C TO CONTINUE.
C
NOW TRY ONE ON YOUR OWN:

2WHAT IS THE GREATEST COMMON FACTOR OF 9 AND 6?
3

GREAT.
DNOTICE THAT 9 AND 6 ARE BOTH FACTORABLE BY 1 AND 3.  THE LARGER
>OF THESE IS 3 WHICH IS CALLED THE GREATEST COMMMON FACTOR.
"THE CORRECT ANSWER IS THEN 3.
6WHAT IS THE GREATEST COMMON FACTOR OFF 12 AND 15?
3
$TERRIFIC.  NOW TO THE NEXT STEP.
<THE CORRECT ANSWER IS 3.  THIS IS  THE LARGEST NUMBER  
4THAT CAN BE DIVIDED EVENLY INTO BOTH 12 AND 15.
2FIND THE GREATEST COMMON FACTOR OF 20 AND 15.
5
FANTASTIC.
>THE CORRECT ANSWER IS 5.  LET'S TRY A LITTLE MORE REVIEW.
2FIND THE GREATEST COMMON FACTOR OF 24 AND 16.
8

GOOD.
>THE CORRECT ANSWER IS 8.  LET'S TRY A LITTLE MORE REVIEW.
DIF WE LOOK AT 9 AND 12 WE FIND THE GREATEST COMMON FACTOR IS 3.

&    9 CAN BE DIVIDED EVENLY BY 3.
&    12 CAN BE DIVIDED EVENLY BY 3.

DWHEN WE DIVIDE THE ORIGINAL NUMBER BY THE GREATEST COMMON FACTOR
<OF 3 THE OTHER FACTOR FOR EACH NUMBER CAN BE CALLED THE
OTHER OR SECOND FACTOR.

$PRESS THE LETTER C TO CONTINUE.
C
0THE GREATEST COMMON FACTOR OF 9 AND 12 IS 3.
$    THE SECOND FACTOR OF 9 IS 3.
$    THE SECOND FACTOR OF 12 IS ?
4
RIGHT ON.
:HINT:  THE OTHER NUMBER THAT WHEN MULTIPLIED BY 3 IS 
EQUAL TO 12?
2THE GREATEST COMMON FACTOR OF 24 AND 28 IS 4.
&    THE SECOND FACTOR OF 24 IS 6.
$    THE SECOND FACTOR OF 28 IS ?
7


GOOD.
4HINT:  THE SECOND FACTOR IS THE FUMBER THAT WHEN
<MULTIPLIED BY THE GREATEST COMMON FACTOR IS EQUAL TO 28.
2THE GREATEST COMMON FACTOR OF 27 AND 21 IS 3.
$   THE SECOND FACTOR OF 27 IS 9.
$   THE SECOND FACTOR OF 21 IS ?
7

GREAT.
BHINT:  THE SECOND FACTOR IS THE NUMBER THAT WHEN MULTIPLIED BY
.THE GREATEST COMMON FACTOR IS EQUAL TO 21.
2THE GREATEST COMMON FACTOR OF 14 AND 28 IS 14.
,     THE SECOND FACTOR OF 24 IS THEN 2.
*     THE SECOND FACTOR OF 12 IS THEN ?
1
TERRIFIC!!!!!!!
>HINT:  THE SECOND FACTOR IS THE  NUMBER THAT IS MULTIPLIED
6        BY THE GREATEST COMMON FACTOR TO EQUAL 12.
>NOW THAT YOU CAN FIND THEE GREATEST COMMON FACTOR AND THE
.SECOND FACTOR YOU SOULD BE ABLE TO FACTOR.

>PRESS THE LETTER C TO CONTINUE AND LET'S SEE HOW IT WORKS.
C
$WE WOULD LIKE TO FACTOR:   9X+15

DTHE GREATEST COMMON FACTOR IS LOCATED IN FRONT, WITH THE SECOND
(FACTORS BEING LOCATED INSIDE THE ().

> THE GREATEST COMMON     SECOND FACTORS ARE LOCATED IN ()
6      FACTOR             SEPARATED BY + OR - SIGNS
$                   3      (3X+5)

$PRESS THE LETTER C TO CONTINUE.
C
@IF WE WOULD LIKE TO FACTOR 9X+12, WHERE THE GREATEST COMMON 
@FACTOR IS 3, WHAT NUMBER WOULD GO IN FRONT OF THE () SIGNS?
3
CORRECT.
BREMEMBER THAT THE GREATEST COMMON FACTOR SHOULD BE LOCATED IN
6FRONT OF THE () AND SHOULD BE FACTORED OUT FIRST.
HIN 9X+12 WHERE 3 IS THE GREATEST COMMON FACTOR THE SECOND FACTOR IS?

(3X+4)
THAT'S TERRIFIC.
3X+4
THAT'S TERRIFIC.
"THE CORRECT ANSWER IS (3X+4).
$PRESS THE LETTER C TO CONTINUE.
C
FRIE04*PLEASE PRESS THE LETTER C TO CONTINUE.
3, WHAT NUMBER WOULD GO IN FRONT OF THE () SIGNS?
3
CORRECT.
BREMEMBER THAT THE GREATEST COMMON FACTOR SHOULD BE LOCATED IN
6FRONT OF THE () AND SHOULD BE FACTORED OUT FIRST.
HIN 9X+12 WHERE 3 IS THE GREATEST COMMON FACTOR THE SECOND FACTOR IS?

(3X+4)
THAT'S TERRIFIC.
3X+4
THAT'S TERRIFI