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$EFINITION ! POLYNOMIAL WITH TWO OR MORE TERMS IS A
PRIME POLYNOMIAL IF IT Ê V>ÌÊ ÊBE WRITTEN AS A PRODUCT
OF POLYNOMIALS OF LESSER DEGREE USING ONLY INTEGER
COEFFICIENTS AND CONSTANTS AND IF THE ONLY COMMON
FACTORS OF ITS TERMS ARE Ê £Ê AND Ê £Ê %XAMPLE X X Ê ÃÊÌÊ A PRIME POLYNOMIAL
BECAUSE Ê {Ê IS A COMMON FACTOR OF ALL ITS TERMS
$EFINITION ! POLYNOMIAL IS FACTORED COMPLETELY IF IT IS
WRITTEN AS A MONOMIAL OR THE PRODUCT OF A MONOMIAL
AND ONE OR MORE Ê «ÀiÊ ÊPOLYNOMIALS
%XAMPLE X X zX IS NOT FACTORED COMPLETELY
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3UM OF 4WO #UBES
AzzB AzzBAzzAB B
%XAMPLE
X X Ê Ý ÓÊÊÓÝÊÊ{Ê $IFFERENCE OF 4WO #UBES
A B A BA AB B
%XAMPLE
X X Ê {Ý ÓÊÊÓÝÊÊ£Ê %XAMPLE &ACTOR THE SUM OR DIFFERENCE OF TWO CUBES
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$IFFERENCE OF
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A Z Z Ê xÎÊ
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B Y Y Y Ê ÓÇÞ ÎÊÊÈ{Ê Y;Ê ÎÞ® ÎÊ Ê { ÎÊ =
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CUBES
YÊ ÎÞÊÊ{Ê Ê Þ ÓÊÊ£ÓÞÊÊ£ÈÊ #HECKPOINT &ACTOR THE POLYNOMIAL COMPLETELY
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%XAMPLE &ACTOR BY GROUPING
&ACTOR THE POLYNOMIAL X X X COMPLETELY
X X X z z X Ê ÝÊÊÓÊ Ê ÝÊÊÓÊ &ACTOR BY GROUPING
z z Ý ÓÊÊ®ÝÊÊÓ®Ê
$ISTRIBUTIVE PROPERTY
z z Ê ÝÊÊήÝÊÊήÝÊÊÓ®Ê
$IFFERENCE OF TWO
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%XAMPLE &ACTOR POLYNOMIALS IN QUADRATIC FORM
&ACTOR COMPLETELY A X AND
B Y Y Y A X Ê {Ý ÓÊ Ê £ÈÊ Ê {Ý ÓÊÊ£È{Ý ÓÊÊ£ÈÊ
Ê {Ý ÓÊÊ£ÈÓÝÊÊ{ÓÝÊÊ{Ê
B Y Y Y Y Ê Þ {ÊÊxÞ ÓÊÊÈÊ Ê ÎÞ ÎÞ ÓÊÊÎÞ ÓÊÊÓÊ
#HECKPOINT &ACTOR EACH POLYNOMIAL COMPLETELY
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%XAMPLE X X Ê Ý ÓÊÊxÝÊÊήÝÊÊή
3OLVE A POLYNOMIAL EQUATION
7HAT ARE THE REALNUMBER SOLUTIONS OF THE EQUATION
X X X X 7RITE ORIGINAL
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Ê Ý {ÊÊ£äÝ ÓÊÊÊ 7RITE IN STANDARD
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Ê Ý ÓÊÊÝ ÓÊÊ£Ê &ACTOR TRINOMIAL
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