&ACTOR AX BX C
'OAL
9OUR .OTES
+ &ACTOR TRINOMIALS OF THE FORM AX BX C
%XAMPLE &ACTOR WHEN B IS NEGATIVE AND C IS POSITIVE
&ACTOR X X 3OLUTION
"ECAUSE B IS NEGATIVE AND C IS POSITIVE BOTH FACTORS OF
C MUST BE Ê ˜i}>̈ÛiÊ 9OU MUST CONSIDER THE Ê œÀ`iÀÊ
OF THE FACTORS OF BECAUSE THE XTERMS OF THE POSSIBLE
FACTORIZATIONS ARE DIFFERENT
&ACTORS
OF &ACTORS
OF 0OSSIBLE
FACTORIZATION
Ê xÊ
X XÊzxÊ ÊÊÊ xÝÊ X Ê ÇÝÊ
Ê £Ê
X XÊz£Ê ÊÊÊ ÝÊ X Ê ££ÝÊ
-IDDLE TERM WHEN
MULTIPLIED
X X X Ê xÊ XÊ z£Ê %XAMPLE &ACTOR WHEN B IS POSITIVE AND C IS NEGATIVE
&ACTOR N N 3OLUTION
"ECAUSE B IS POSITIVE AND C IS NEGATIVE THE FACTORS OF
C HAVE Ê `ˆvviÀi˜ÌÊÈ}˜ÃÊ &ACTORS
OF &ACTORS
OF 0OSSIBLE
FACTORIZATION
-IDDLE TERM WHEN
MULTIPLIED
Ê ÎÊ N NÊzÎÊ Ê ÊÊÊΘÊzx˜ÊzӘÊÊÊÊ
Ê ÎÊ
N NÊzÎÊ Ê ÊÊÊΘÊzx˜ÊzӘÊÊÊÊ
Ê £Ê N NÊz£Ê Ê ˜Êz£x˜Êz£{˜Ê
Ê £Ê
N NÊz£Ê Ê ˜Êz£x˜Êz£{˜Ê
N N Nz Ê£Ê Nz ÊÎÊ #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
#HECKPOINT &ACTOR THE TRINOMIAL
X X M M ­ÝÊÊ£®­ÎÝÊÊÓ®Ê
%XAMPLE Ê ­“ÊÊή­Ó“ÊÊÇ®
&ACTOR WHEN A IS NEGATIVE
&ACTOR X X 3OLUTION
3TEP &ACTOR Ê £Ê FROM EACH TERM OF THE TRINOMIAL
X X Ê Ê Ê {Ý ÓÊÊ{ÝÊÊÎÊ 3TEP &ACTOR THE TRINOMIAL Ê {Ý ÓÊÊ{ÝÊÊÎÊ "ECAUSE B
AND C ARE BOTH Ê ˜i}>̈ÛiÊ THE FACTORS OF C MUST
HAVE Ê `ˆvviÀi˜ÌÊÈ}˜ÃÊ 2EMEMBER TO
INCLUDE THE Ê £Ê
THAT YOU FACTORED
OUT IN 3TEP &ACTORS
OF &ACTORS
OF 0OSSIBLE
FACTORIZATION
-IDDLE TERM WHEN
MULTIPLIED
Ê ÎÊ
X XÊzÎÊ Ê Ê ÊÊÊÎÝÊz{ÝÊzÝÊÊÊ Ê
Ê £Ê
X XÊz£Ê Ê ÊÊÝÊz£ÓÝÊz££ÝÊÊ
Ê ÎÊ
X XÊzÎÊ Ê Ê ÊÊÊÎÝÊz{ÝÊzÝÊÊÊ Ê
Ê £Ê
X XÊz£Ê Ê ÊÊÝÊz£ÓÝÊz££ÝÊÊÊ
Ê ÎÊ X XÊzÎÊ Ê ÈÝÊzÓÝÊz{ÝÊ
Ê ÎÊ
X XÊzÎÊ Ê Ê ÊÊÊÈÝÊzÓÝÊz{ÝÊÊÊÊ Ê
X X Ê ­ÓÝÊÊ£®­ÓÝÊÊήÊ
#HECKPOINT #OMPLETE THE FOLLOWING EXERCISE
&ACTOR Y Y ­ÓÞÊÊ£®­ÞÊÊx®
,ESSON s !LGEBRA .OTETAKING 'UIDE
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
9OUR .OTES
%XAMPLE 7RITE AND SOLVE A POLYNOMIAL EQUATION
4ENNIS !N ATHLETE HITS A TENNIS BALL AT AN INITIAL HEIGHT OF
FEET AND WITH AN INITIAL VERTICAL VELOCITY OF FEET PER
SECOND
A 7RITE AN EQUATION THAT GIVES THE HEIGHT IN FEET OF THE
BALL AS A FUNCTION OF THE TIME IN SECONDS SINCE IT LEFT
THE RACKET
B !FTER HOW MANY SECONDS DOES THE BALL HIT THE GROUND
3OLUTION
A 5SE THE Ê ÛiÀ̈V>Ê“œÌˆœ˜Ê“œ`iÊ TO WRITE AN EQUATION
FOR THE HEIGHT H IN FEET OF THE BALL
H T VT S
Ê 6iÀ̈V>Ê“œÌˆœ˜ÊÊ
“œ`iÊ
H T Ê ÈÓÊ T Ê nÊ
V Ê ÈÓÊ AND S Ê nÊ
B 4O FIND THE NUMBER OF SECONDS THAT PASS BEFORE THE
BALL LANDS FIND THE VALUE OF T FOR WHICH THE HEIGHT
OF THE BALL IS Ê äÊ 3UBSTITUTE Ê äÊ FOR H AND SOLVE THE
EQUATION FOR T
Ê äÊ T Ê ÈÓÊ T Ê nÊ
3UBSTITUTE Ê äÊ FOR H
Ê äÊ Ê ÓÊ Ê nÌ ÓÊÊΣÌÊÊ{Ê &ACTOR OUT Ê ÓÊ Ê äÊ Ê ÓÊ Ê nÌ ÊÊ£Ê Ê Ì ÊÊ{Ê &ACTOR THE TRINOMIAL
Ê nÌÊÊ£ÊÊäÊ
:EROPRODUCT PROPERTY
OR Ê ÌÊÊ{ÊÊä
£
n
Ê Êz OR
Ê ÌÊÊÊ]
Ê ÌÊÊ{Ê
3OLVE FOR T
! NEGATIVE SOLUTION DOES NOT MAKE SENSE IN THIS SITUATION
4HE TENNIS BALL HITS THE GROUND AFTER Ê {ÊÃiVœ˜`ÃÊ #HECKPOINT #OMPLETE THE FOLLOWING EXERCISE
(OMEWORK
7HAT )F )N %XAMPLE SUPPOSE ANOTHER ATHLETE
HITS THE TENNIS BALL WITH AN INITIAL VERTICAL VELOCITY
OF FEET PER SECOND FROM A HEIGHT OF FEET !FTER
HOW MANY SECONDS DOES THE BALL HIT THE GROUND
£°xÊÃiVœ˜`Ã
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
,ESSON s !LGEBRA .OTETAKING 'UIDE