Answer :
Option B, which is 3x⁴ + 9x³ − 6x², has 3x² as the Greatest Common Factor of its terms.
The question asks which of the given trinomials has 3x² as the Greatest Common Factor (GCF) of its terms. The GCF is the highest monomial that divides evenly into each term of the polynomial.
Let's analyze each option:
- A. 9x⁵ − 18x⁴ + 27x³ does not have 3x² as the GCF because the smallest exponent of x is 3, and the coefficients have a GCF of 9.
- B. 3x⁴ + 9x³ − 6x² does have 3x² as the GCF because every term can be divided by 3x², leaving us with whole numbers and variables with non-negative exponents in the simplified form.
- C. 9x⁴ + 12x³ − 6x does not have 3x² as the GCF because the last term does not contain the variable x squared.
- D. 3x⁵ + 9x⁴ − 6x³ does not have 3x² as the GCF for similar reasons as option A, where the smallest exponent of x is 3, and the coefficients have a GCF of 3.
Therefore, the answer is B. 3x⁴ + 9x³ − 6x².
