Final answer:
The division of the polynomial 2x⁵ · 5x³ by x results in the polynomial 10x⁷, applying rules of Division of Exponentials by subtracting exponents.
Step-by-step explanation:
To divide the polynomials 2x⁵ · 5x³ by x, we use the rules of Division of Exponentials. First, we divide the digit terms of the numerator by the digit term of the denominator. In this case, we have 2 multiplied by 5, which gives us 10. Then, we subtract the exponents of the exponential terms, where the exponent of the x in the denominator is understood to be 1. Thus, we get the exponent for x in the result by subtracting 1 from the sum of the exponents in the numerator: 5 + 3 - 1. This gives us 2x⁷.
The process mirrors when we multiply exponentials, for example, (5³)⁴ equals 5¹², indicating that we multiple exponents. Similarly, with division, we subtract exponents. Applying these principles, the finalized expression after dividing 2x⁵ · 5x³ by x is 10x⁷.