What is the product of the prime polynomials 8x^3 and 2x?

To find the product of the prime polynomials 8x³ and 2x, we will use the basic principles of polynomial multiplication.

First, let’s break down the two polynomials:

• 8x³: This means 8 times x raised to the power of 3.
• 2x: This means 2 times x raised to the power of 1.

When multiplying these two polynomials, we follow these steps:

1. Multiply the numerical coefficients (the numbers in front):
• 8 (from 8x³) multiplied by 2 (from 2x) equals 16.
2. Now, multiply the variable parts:
• x³ (from 8x³) multiplied by x (from 2x) equals x³ * x¹ = x³⁺¹ = x⁴.

Putting it all together, the product is:

16x⁴

Thus, the product of the prime polynomials 8x³ and 2x is 16x⁴.