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Answer :
The correct trinomial that has 3x² as the GCF of its terms is Option B: 3x⁴ + 9x³ − 6x². This is because 3x² can be factored out from each term of the trinomial, making it the highest power of x with the coefficient 3 common to all terms.
The student is asking which trinomial has 3x² as the greatest common factor (GCF) of its terms. To find the trinomial with 3x² as the GCF, we need to look for the highest power of x that is in common with the coefficient 3 in all the terms of the trinomial.
Option A: 9x⁵ − 18x⁴ + 27x³ has x³ as the GCF, not 3x².
Option B: 3x⁴ + 9x³ − 6x² has 3x² as the GCF as it is the highest power of x that can be factored out from all terms.
Option C: 9x⁴ + 12x³ − 6x has 3x as the GCF.
Option D: 3x⁵ + 9x⁴ − 6x³ has 3x³ as the GCF.
Therefore, the correct answer is Option B: 3x⁴ + 9x³ − 6x² as it has 3x² as the GCF of its terms.
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