&ACTOR 3PECIAL 0RODUCTS
'OAL
+ &ACTOR SPECIAL PRODUCTS
6/#!"5,!29
9OUR .OTES
0ERFECT SQUARE TRINOMIAL ÊÌÀ>ÊvÊÌ
iÊvÀÊÊ
> ÓÊÊÓ>LÊÊL ÓÊÀÊ> ÓÊÊÓ>LÊÊL Ó
$)&&%2%.#% /& 47/ 315!2%3 0!44%2.
!LGEBRA
A B A BÊ >ÊÊLÊ %XAMPLE
X X Ê ÎÝÊÊÓÊ Ê ÎÝÊÊÓÊ %XAMPLE &ACTOR THE DIFFERENCES OF TWO SQUARES
&ACTOR THE POLYNOMIAL
A Z Z Ê Ê Z Ê Ê Z Ê Ê B X Ê {ÝÊ Ê ÎÊ zÊ {ÝÊ Ê ÎÊ Ê {ÝÊ Ê ÎÊ C A B A Ê xLÊ A Ê xLÊ A Ê xLÊ D N Ê {Ê Ê £Ê Ê { ÓÊ Ê {Ê ;Ê £Ê Ê ÓÊ =
zÊ {Ê Ê £Ê Ê ÓÊ Ê £Ê Ê ÓÊ #HECKPOINT &ACTOR THE POLYNOMIAL
X Ê
Ê ÝÊÊ£ä®ÝÊÊ£ä®Ê
C D
Ê
Ê VÊÊÎ` ®VÊÊÎ` ®Ê
,ESSON s !LGEBRA .OTETAKING 'UIDE
Y Ê ÇÞÊÊx®ÇÞÊÊx®
M
Ê xÎÊÊ{®ÎÊÊ{®
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
9OUR .OTES
0%2&%#4 315!2% 42)./-)!, 0!44%2.
!LGEBRA
A AB B Ê >ÊÊLÊ A AB B Ê >ÊÊLÊ %XAMPLE
X X X X + Ê ÝÊÊ{Ê X X X X + Ê ÝÊÊÎÊ %XAMPLE &ACTOR PERFECT SQUARE TRINOMIALS
&ACTOR THE POLYNOMIAL
A X X X Ê ÝÊ+ÊnÊ Ê nÊ Ê ÝÊÊnÊ B Y Y Ê ÓÞÊ Ê ÓÞÊ+ÊÎÊ Ê ÎÊ zÊ ÓÞÊÊÎÊ C S ST T Ê ÎÃÊ Ê ÎÃÊ+ÊÌÊ Ê ÌÊ Ê ÎÃÊÊÌÊ D Z Z z Ê ÎÊ Z zZ Ê ÎÊ ;Z zÊ âÊ+Ê{Ê Ê {Ê =
zÊ ÎÊ Ê âÊÊ{Ê #HECKPOINT &ACTOR THE POLYNOMIAL
X X Ê
Ê ÝÊÊÇ®ÓÊ
X XY Y Ê
Ê {ÝÊÊxÞ®ÓÊ
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
Y Y Ê ÎÞÊÊ£®Ó
R R Ê xÀÊÊÓ®Ó
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
%XAMPLE 3OLVE A POLYNOMIAL EQUATION
3OLVE THE EQUATION X X ]z X X ]z 7RITE ORIGINAL EQUATION
Ê {Ý ÓÊÊ{ÝÊÊ£Ê -ULTIPLY EACH SIDE
BY Ê {Ê Ê ÓÝ ®ÓÊÊÓÓÝÊ+Ê£®ÊÊ£ÓÊ 7RITE LEFT SIDE AS
A AB B Ê ÓÝ ÊÊ£®ÓÊ 0ERFECT SQUARE
TRINOMIAL PATTERN
4HIS EQUATION
HAS TWO IDENTICAL
SOLUTIONS BECAUSE
IT HAS TWO IDENTICAL
FACTORS
Ê ÓÝ ÊÊ£Ê :EROPRODUCT PROPERTY
£
Ó
X Ê ÊÊ]Êz
%XAMPLE 3OLVE FOR X
3OLVE A VERTICAL MOTION PROBLEM
&ALLING /BJECT ! BRICK FALLS OFF OF A BUILDING FROM A HEIGHT
OF FEET !FTER HOW MANY SECONDS DOES THE BRICK LAND
ON THE GROUND
3OLUTION
5SE THE VERTICAL MOTION MODEL 4HE BRICK FELL SO ITS
INITIAL VERTICAL VELOCITY IS Ê äÊ &IND THE VALUE OF TIME
T IN SECONDS FOR WHICH THE HEIGHT H IN FEET IS Ê äÊ H Ê £ÈÌ ÓÊÊÛÌÊÊÃÊ
6ERTICAL MOTION MODEL
Ê äÊ Ê £ÈÌ ÓÊÊäÌÊÊ£{{Ê
3UBSTITUTE VALUES
Ê äÊ Ê £ÈÊ Ê Ì ÓÊÊÊ &ACTOR OUT Ê £ÈÊ Ê äÊ Ê £ÈÊ Ê ÌÊÊÎÊ Ê ÌÊÊÎÊ $IFFERENCE OF TWO
SQUARES
Ê ÌÊÊÎÊÊäÊ
OR Ê ÌÊÊÎÊÊäÊ
Ê ÌÊÊÎÊ OR
Ê ÌÊÊÎÊ
:EROPRODUCT PROPERTY
3OLVE FOR T
4HE BRICK LANDS ON THE GROUND Ê ÎÊÃiV`ÃÊ AFTER IT FALLS
,ESSON s !LGEBRA .OTETAKING 'UIDE
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
9OUR .OTES
#HECKPOINT 3OLVE THE EQUATION
M M Ê
Ê {
W W Ê
Ê n
T Ê
Ê ££
#HECKPOINT #OMPLETE THE FOLLOWING EXERCISE
7HAT )F )N %XAMPLE SUPPOSE THE BRICK FALLS FROM
A HEIGHT OF ]zFEET !FTER HOW MANY SECONDS DOES
THE BRICK LANDS ON THE GROUND
£x
n
]ÊÊÊz ÃiV`Ã
(OMEWORK
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
,ESSON s !LGEBRA .OTETAKING 'UIDE
© Copyright 2026 Paperzz