**Unformatted text preview: **coefficients. That is, the factors must be prime (or irreducible ) over the integers. • In Chapter 2, we will factor over other sets, such as ± , ± , or ± . TIP 1 : The Greatest Common Factor (GCF) , if it is not 1, should typically be factored out first, although it can be factored out piece-by-piece for more complicated expressions. (Unfortunately, there is no simple, standard definition for the GCF.) Example 1 (Factoring out a GCF) We factor 8 x + 6 as 2 4 x + 3 ( ) , because 2 is the GCF. 2 is the greatest common divisor of 8 and 6. § Example 2 (Factoring out a GCF) We factor x 5 + x 3 as x 3 x 2 + 1 ( ) , because x 3 is the GCF. x 3 is the power of x with the least exponent. §...

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