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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