&ACTOR X BX C
'OAL
9OUR .OTES
+ &ACTOR TRINOMIALS OF THE FORM X BX C
&!#4/2).' X BX C
!LGEBRA
X BX C X PX Q PROVIDED Ê «ÊÊµÊ B
AND Ê «µÊ C
%XAMPLE
X X Ê ÝÊÊxÊ Ê ÝÊÊ£Ê BECAUSE Ê xÊÊ£Ê AND Ê xÊ+Ê£Ê &ACTOR WHEN B AND C ARE POSITIVE
%XAMPLE &ACTOR X X 3OLUTION
&IND TWO Ê «œÃˆÌˆÛiÊ FACTORS OF Ê £ÈÊ WHOSE SUM IS Ê £äÊ -AKE AN ORGANIZED LIST
&ACTORS OF
Ê £ÈÊ
3UM OF FACTORS
Ê £Ê
Ê ÓÊ
Ê {Ê
Ê £Ê Ê £ÇÊ
Ê ÓÊ Ê £äÊ
Ê {Ê Ê nÊ
4HE FACTORS AND Ê ÓÊ HAVE A SUM OF Ê £äÊ SO THEY ARE
THE CORRECT VALUES OF P AND Q
X X X Ê ÝÊÊÓÊ #(%#+
X Ê ÝÊÊÓÊ Ê Ý ÓÊÊÓÝÊÊnÝÊÊ£ÈÊ
Ê Ý ÓÊÊ£äÝÊÊ£ÈÊ
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
-ULTIPLY
3IMPLIFY
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
&ACTOR WHEN B IS NEGATIVE AND C IS POSITIVE
%XAMPLE &ACTOR A A 3OLUTION
"ECAUSE B IS NEGATIVE AND C IS POSITIVE P AND Q
MUST Ê LœÌ…ÊLiʘi}>̈ÛiÊ &ACTORS OF
Ê ÈÊ
3UM OF FACTORS
Ê È]Ê£Ê
Ê ÈÊ Ê £Ê Ê ÇÊ
Ê Î]ÊÓÊ
Ê ÎÊ Ê ÓÊ Ê xÊ
A A Ê >ÊÊÎÊ Ê >ÊÊÓÊ &ACTOR WHEN B IS POSITIVE AND C IS NEGATIVE
%XAMPLE &ACTOR Y Y 3OLUTION
"ECAUSE C IS NEGATIVE P AND Q MUST Ê …>ÛiÊ`ˆvviÀi˜ÌÊ
È}˜ÃÊ &ACTORS OF
Ê £äÊ
3UM OF FACTORS
zzzzzz Ê £Ê
z zzzzzzzz Ê £Ê
zzzzzzz Ê ÓÊ
zzzzzzz Ê ÓÊ
Ê £Ê Ê ™Ê
Ê ­£®Ê Ê ™Ê
Ê ÓÊ Ê ÎÊ
Ê ­Ó®Ê Ê ÎÊ
Y Y Ê ÞÊÊxÊ Ê ÞÊÊÓÊ #HECKPOINT &ACTOR THE TRINOMIAL
X X ­ÝÊÊ{®­ÝÊÊήÊ
,ESSON s !LGEBRA .OTETAKING 'UIDE
X X Ê ­ÝÊÊn®­ÝÊÊ£®
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
9OUR .OTES
#HECKPOINT &ACTOR THE TRINOMIAL
X X X X ­ÝÊʙ®­ÝÊÊήÊ
Ê ­ÝÊÊx®­ÝÊÊ{®
Ê Y Y Z Z ­ÞÊÊÇ®­ÞÊÊήÊ
%XAMPLE Ê ­âÊÊÈ®­âÊÊ{®
3OLVE A POLYNOMIAL EQUATION
3OLVE THE EQUATION X X X X X X Ê £nÊ 7RITE ORIGINAL EQUATION
3UBTRACT Ê £nÊ FROM EACH
SIDE
Ê ­ÝÊʙ®­ÝÊÊÓ®Ê &ACTOR LEFT SIDE
Ê ÝÊʙÊzäÊ
:EROPRODUCT PROPERTY
OR Ê ÝÊÊÓÊzäÊ
Ê ÝÊÊ™Ê OR
Ê ÝÊÊÓÊ
3OLVE FOR X
4HE SOLUTIONS OF THE EQUATION ARE Ê ™Ê>˜`ÊÓÊ #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
%XAMPLE 3OLVE A MULTISTEP PROBLEM
$IMENSIONS 4HE BANDAGE SHOWN
HAS AN AREA OF SQUARE
CENTIMETERS &IND THE WIDTH OF
THE BANDAGE
3OLUTION
3TEP 7RITE AN EQUATION USING THE FACT THAT THE AREA OF
THE BANDAGE IS SQUARE CENTIMETERS
!*+W
&ORMULA FOR AREA
Ê £ÈÊ Ê ­ÎÊÊÜÊÊÎ®Ê + W
Ê Ü ÓÊÊÈÜÊÊ£ÈÊ
3UBSTITUTE VALUES
3IMPLIFY
3TEP 3OLVE THE EQUATION FOR W
Ê Ü ÓÊÊÈÜÊÊ£ÈÊ
7RITE EQUATION
Ê ­Ü ÊÊn®­ÜÊÊÓ®Ê
&ACTOR RIGHT SIDE
Ê ÜÊÊnÊÊäÊ
OR Ê ÜÊÊÓÊÊäÊ
:EROPRODUCT
PROPERTY
Ê ÜÊÊnÊ
OR
Ê ÜÊÊÓÊ
3OLVE FOR W
4HE BANDAGE CANNOT HAVE A NEGATIVE WIDTH SO THE WIDTH
IS Ê ÓÊVi˜Ìˆ“iÌiÀÃÊ #HECKPOINT #OMPLETE THE FOLLOWING EXERCISES
3OLVE THE EQUATION S S Ê
(OMEWORK
Ê £]Ê£Î
7HAT )F )N %XAMPLE SUPPOSE THE AREA OF THE
BANDAGE IS SQUARE CENTIMETERS 7HAT IS THE
WIDTH
ÎÊVi˜Ìˆ“iÌiÀÃ
,ESSON s !LGEBRA .OTETAKING 'UIDE
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY