Final answer:
The greatest common factor (GCF) of the terms in the polynomial 4x⁴ - 32x³ - 60x² is 4x²(x - 5)(x + 3).
Step-by-step explanation:
The greatest common factor (GCF) of the terms in the polynomial 4x⁴ - 32x³ - 60x² can be found by factoring out the common factors of the terms. First, we can factor out the common factor of 4x² from each term:
4x⁴ - 32x³ - 60x² = 4x²(x² - 8x - 15)
Next, we can factor the quadratic expression inside the parentheses to find the GCF:
x² - 8x - 15 = (x - 5)(x + 3)
Therefore, the GCF of the terms in the polynomial is 4x²(x - 5)(x + 3).
First, factor out the greatest power of x that is common to all terms, which is x². Then, find the greatest common divisor of the numerical coefficients 4, 32, and 60. Since all coefficients are multiples of 4, that is the greatest common divisor.
The GCF of the terms in the given polynomial is 4x².