math 10 · 2019. 11. 29. · math 10 notes - 5.2 common factors common factors the factors of a...
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Math 10
NOTES - 5.2 Common Factors
Common Factors
The factors of a term (ex: 35x2) are numbers (or variables) that can be
multiplied to give that term.
Write the factors for each term:
Common factors:
Common factors are "factors" that are shared by two or more terms.
Greatest Common Factor (GCF) : is the largest shared factor. or :.
a) 25 and 40 c) XS
'd-5 e \) ~S)~40 -: \:> L.\. 0 , 'l, ?0 ) 1-\) \ \) )f)~
bC~\S®
and X2
j. S : rJ;3) '-A- 'I~ X1.2 :~
C;~ \S ;<2.
Examples:
12x4 and 8x3
\2 'il.\ ~ \ l \1\ L \~\ 3 \6)t~~ b.3'i.3: \,'6, ?-\®)~)(-9bcF\~ y-y--3
Least Common Multiple (LCM): is the smallest multiple (the smallest number thatboth terms "go into").
15 and 10 6 and 8
\y..b =- Co;). 1- Co e, \L
3~6 ~ \t:>L\1'(o::@
LC\J\
\ ~\5= \S
d--"" \5 ~®3,,\5::.. 4-5
\ '1--\0 e: \0
~ 1--\.0 z: ~O
3 1-l0~®LLM \s 30
Factoring Polynomials
\ l' 15=- 8;;..~ «)= \~
3 ~f>:@
We already learned how to expand a po~l~yn~o~m!..!.!iE.!al,-,-.__ -~Ex: ~) = J \ ",2- - 2 '8 'f.. L
~FCt.c.-\--Ov -:-e '.Factoring is the reverse of expanding/ multiplying.To factor a polynomial, you must find the GCF and bring it outside of the brackets.
Examples of Factoring
l + 8xy + 2y
(3c.,~\~ '/
'j(j"" ~ ~ -+ 2-)
16x2y + 24xl + 8xy
bcr= v S bXj
3 ~~( ~)( '+ ~~ * \')
27r2s2- 18r3s2- 36rs3
~ Cf \ s ~ r-S 2-
C\rs2(3\ _~\2- -Lt5)
2
Determine Binomial Factors
Same process is used. Find the GCF and write your answer as a product ofbinomials.
Examples:
3x(x - 4) + 5(0) 5a(a +2) - 2(a + 2)
~cs:,~ l'"-L\- J
("t-L\ )(3~i-5)~a= \$ (CA-\-Lj{
( Q-\-~)(5Q-~)
,("(j 2. -\' ~ ~:J)+~~~\b.'-...:.-~ ~, .
~ (:1 -\ ~:c) 4- ~ (~ -\- '6 'f.. ')
E'AC;~ \ s (~ -t <0 t<J(~--\ 13 'I< ) (j -\-~)
Do 5.2 Questions "Factoring"
3
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