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The idea that some polynomials cannot be factored at all is compared to which fact about numbers?
ASome numbers are negative and reverse all signs
BSome numbers are even and divide by two
CSome numbers are fractions and simplify further
DSome numbers are prime and have no factor pairs
Answer & Solution
Correct answer: D. Some numbers are prime and have no factor pairs
1. Just as some numbers, like 7 or 13, have only themselves and 1 as factors, some polynomials have no factor pairs either.
2. Such numbers are called prime, and the source applies the same idea to polynomials that cannot be broken into a product of smaller polynomials.
3. A prime polynomial is not related to whether its coefficients are negative, even, or fractional; it is about having no valid factorization at all.
_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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