Final answer:
The greatest common factor of the polynomial 8x + 14x - 32 is 2x(11).
Step-by-step explanation:
The greatest common factor (GCF) of a polynomial is the largest number or expression that divides evenly into each term of the polynomial. In this case, the polynomial is 8x + 14x - 32.
To find the GCF, we need to factor out any common factors from the terms. The terms 8x and 14x have a common factor of 2x. So, we can factor out 2x from these terms: 2x(4 + 7) = 2x(11).
Next, we can look at the constant term -32. The only common factor it has with 2x(11) is 1. So, the GCF of the polynomial 8x + 14x - 32 is 2x(11).