What is the greatest common factor of the terms in the polynomial 4x^4, 32x^3, 60x^2?

The greatest common factor (GCF) of the terms in the polynomial 4x⁴, 32x³, and 60x² is 4x².

To find the GCF, we start by determining the coefficients and the variable portions of each term.

• The coefficients are 4, 32, and 60. The GCF of these numbers is 4, since:
• 4 can be divided by 4 (4 ÷ 4 = 1)
• 32 can be divided by 4 (32 ÷ 4 = 8)
• 60 can also be divided by 4 (60 ÷ 4 = 15)
• Next, we look at the variable parts: x⁴, x³, and x².
• The smallest exponent among these is 2. Thus, the GCF of the variable part is x².

Putting it all together, the GCF of the polynomial terms is the product of the GCF of the coefficients and the GCF of the variables:

GCF = 4 (from coefficients) × x² (from variables) = 4x².