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When factoring -8y - 24, why must the GCF itself be negative?
ABecause the constant term is larger than the coefficient
BBecause subtraction always produces a negative GCF
CBecause the leading coefficient of the expression is negative
DBecause the variable y has an implied negative sign
Answer & Solution
Correct answer: C. Because the leading coefficient of the expression is negative
1. Ignoring the signs, the GCF of 8y and 24 is 8.
2. Since the expression -8y - 24 has a negative leading coefficient, the GCF is taken as -8 instead of 8.
3. Rewrite each term using -8: -8y is -8 times y, and -24 is -8 times 3.
4. Factor to get -8(y + 3), and check by multiplying: -8 times y plus -8 times 3 gives back -8y - 24.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.1 Greatest Common Factor and Factor by Grouping_
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