Introduction to factoring polynomials

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 8p3 – q3 = (2p)3 – (q)3

a3 – b3

and we have a difference

= (2p – q)((2p)2 + (2p)(q) + (q)2)

 difference of cubes

= (a – b)(a2 + ab + b2)

factors as

= (2p – q)(4p2 + 2pq + q2)

Slide 58

Ex: Factor x3 + 27y9

Notice the terms are both perfect cubes

x3 = (x)3

27y9 = (3y3)3

 x3 + 27y9 = (x)3 + (3y3)3

a3 + b3

and we have a sum

= (x + 3y3)((x)2 - (x)(3y3) + (3y3)2)

 sum of cubes

= (a + b)(a2 - ab + b2)

factors as

= (x + 3y3)(x2 – 3xy3 + 9y6)

Slide 59