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FACTORING GCF’S, DIFFERENCES OF SQUARES, PERFECT SQUARES, AND CUBES
Objectives
You will be able to factor: Greatest common factors Differences of squares Perfect squares Sums and differences of cubes
Greatest common factor (GCF)
Definition:Coefficient and variables that are common to all terms in a polynomial
Ex 1: 34 205 xx 45 3 xx
GCF: 35x
Factored Form:
Ex 2: yxyx 32 2012 GCF:
Factored Form:
yx 24
xyx 534 2
Ex 3: 443526 2410 qpqpqp GCF:
Factored Form:
242 qp
2224 252 qpqpqp
Practice
2332 155 yxyx xyyx 35 22
933 2 yy 33 2 yy
acadab 1246 cdba 6232 352444263 15129 zyxzyxzyx yzzxxyzyx 5433 222242
344453534 352114 cbacbacba
abcbaccba 5327 22333
mmm 64324 34 1684 23 mmm
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Differences of Squares
Formula: bababa 22
Ex 1: 492x 77 xx
Ex 2: 82 94 yx 44 3232 yxyx
Ex 3: 4812 2a 412 2a 2212 aa
Ex 4:
222 2045 zyx 222 495 zyx yzxyzx 23235 Ex 5:
92a PRIME! It’s not a difference!
Sums and Differences of CubesFormula: 2233 babababa
2233 babababa
Ex 1: 83x 22 222 xxx
Try 2: 273y 22 333 yyy 933 2 yyy
Ex 3: 33 278 yx 22 332232 yyxxyx 22 96432 yxyxyx
Try 4: 33 12564 yx 22 554454 yyxxyx 22 25201654 yxyxyx
a=x b=2
Perfect square trinomials
Formula: Figure it out
22x 22 xx 442 xx
23x 33 xx 962 xx
24x 44 xx 1682 xx
How do we go from hereto here?
232x 3232 xx 9124 2 xx
2? ba 2? ba
Perfect square trinomials
Formula: 222 2 bababa 222 2 bababa
23 x962 xxEx 1:
Ex 2: 25102 xx 25 x
Ex 3: 92416 2 xx 234 x
Ex 4: 25309 2 xx 253 x
Ex 5: 49284 2 xx 272 x
Factoring Completely
Always look for a GCF first
Check the result to see if it can be factored further
9162 6 x 79792 33 xx
mmm 18122 35 22 32 mm
2502 3 r )255)(5(2 2 rrr
14 x 1112 xxx
16 x 1111 22 xxxxxx
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