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Answer :
Final answer:
The greatest common factor (GCF) of the polynomial 6x⁵+15x⁴+21x³ is 3x³.
Explanation:
The greatest common factor (GCF) of a polynomial is the largest factor that can divide all the terms of the polynomial. To find the GCF of the polynomial 6x⁵+15x⁴+21x³, we need to find the common factors of the coefficients and the variable exponents.
Step 1: Write down the prime factorization of each coefficient:
6 = 2 × 3
15 = 3 × 5
21 = 3 × 7
Step 2: Find the common factors of the coefficients:
The only common factor is 3.
Step 3: Find the smallest exponent for each variable:
The variable in this polynomial is x, and the exponents are 5, 4, and 3. The smallest exponent is 3.
Step 4: Combine the common factors of the coefficients with the variable raised to the smallest exponent:
The GCF of the polynomial is 3x³.
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