What polynomial can be formed using the factors 4x^7 and x^4?

To find the polynomial that has the factors 4x⁷ and x⁴, we need to multiply these two expressions together.

First, let’s break down what we have:

• The first factor is 4x⁷, which means it is the term 4 multiplied by x raised to the power of 7.
• The second factor is x⁴, meaning it is x raised to the power of 4.

When we multiply these two factors, we follow the rules for multiplying variables and constants:

1. Multiply the coefficients (the numeric parts):
• The coefficient of the first factor is 4, and the second factor does not have a coefficient written explicitly (implicitly it is 1).
• So, 4 (from 4x⁷) times 1 (from x⁴) equals 4.
2. Next, we combine the powers of x. Remember that when multiplying like bases, we add the exponents:
• Here, the exponents are 7 and 4.
• So, we add 7 + 4 = 11.

Putting it all together, the result of multiplying the two factors 4x⁷ and x⁴ gives us:

4x¹¹

Therefore, the polynomial that has 4x⁷ and x⁴ as factors is 4x¹¹.