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)

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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"

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