In this case we do have multiplication so cancel as

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Unformatted text preview: ted to move away from x as the main variable in the examples. Do not get so used to seeing x’s that you always expect them. The problems will work the same way regardless of the letter we use for the variable so don’t get excited about the different letters here. (a) x 2 - 5 x - 14 x2 - 4 ×2 x 2 - 3 x + 2 x - 14 x + 49 Okay, this is a multiplication. The first thing that we should always do in the multiplication is to factor everything in sight as much as possible. ( x - 7) ( x + 2) × ( x - 2) ( x + 2) x 2 - 5 x - 14 x2 - 4 ×2 = 2 2 x - 3 x + 2 x - 14 x + 49 ( x - 2 )( x - 1) ( x - 7) Now, recall that we can cancel things across a multiplication as follows. a ck a c × =× bd bk d Note that this ONLY works for multiplication and NOT for division! In this case we do have multiplication so cancel as much as we can and then do the multiplication to get the answer. ( x + 2) × ( x + 2) = ( x + 2) x 2 - 5 x - 14 x2 - 4 ×2 = 2 x - 3 x + 2 x - 14 x + 49 ( x - 1) ( x - 7 ) ( x - 1)( x - 7 ) 2 [Return to Prob...
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