Factoring with a Negative Leading Coefficient
When factoring a polynomial whose leading coefficient is negative, the GCF is taken as negative. To apply this rule, first ignore the signs of all terms and determine the GCF of their absolute values (including any shared variable factors). Then attach a negative sign to that GCF. When the negative GCF is factored out using the reverse Distributive Property, the signs of all terms inside the parentheses are reversed compared to the original expression — negative terms become positive and positive terms become negative. The same four-step factoring procedure applies: find the (negative) GCF, rewrite each term as a product of the GCF, factor using the reverse Distributive Property, and check by multiplying. For example, to factor , the GCF of and is , but since the leading coefficient is negative, is used as the GCF, yielding .
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