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Unformatted text preview: just use the general process for factoring quadratic
polynomials in this case rather than checking that it was one of the special forms, but we did need
to see one of them worked.
[Return to Problems] (b) 25 x 2 - 9
In this case all that we need to notice is that we’ve got a difference of perfect squares, 25 x 2 - 9 = ( 5 x ) - ( 3)
2 2 So, this must be the third special form above. Here is the correct factoring for this polynomial. 25 x 2 - 9 = ( 5 x + 3) ( 5 x - 3) [Return to Problems] (c) 8 x + 1
This problem is the sum of two perfect cubes,
3 8 x3 + 1 = ( 2 x ) + (1)
3 3 and so we know that it is the fourth special form from above. Here is the factoring for this
polynomial. 8 x 3 + 1 = ( 2 x + 1) ( 4 x 2 - 2 x + 1) [Return to Problems]
© 2007 Paul Dawkins 38 http://tutorial.math.lamar.edu/terms.aspx College Algebra Do not make the following factoring mistake! a 2 + b2 ¹ ( a + b ) 2 This just simply isn’t true for the vast majority of sums of squares, so be careful not to make this
very common mistake. There are rare cases where this can be done, b...
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- Spring '12