Question

b. $(x - 17)^4(x - 45)^6(x - 8472)^8(x - 9373404)^{20}geq0$

Explanation:

Step1: Analyze the nature of even - powered factors

For any real number \(x\) and even positive integer \(n\), \(a^n\geq0\) where \(a\) is a real - valued expression. Here, the exponents \(4\), \(6\), \(8\), and \(20\) are all even positive integers.
The factors \((x - 17)^4\), \((x - 45)^6\), \((x - 8472)^8\), and \((x - 9373404)^{20}\) are non - negative for all real values of \(x\) because for any real number \(y\), if \(n\) is an even positive integer, \(y^n\geq0\).

Step2: Determine the solution set

Since the product \((x - 17)^4(x - 45)^6(x - 8472)^8(x - 9373404)^{20}\) is the product of non - negative real numbers for all real \(x\), the inequality \((x - 17)^4(x - 45)^6(x - 8472)^8(x - 9373404)^{20}\geq0\) is true for all real numbers \(x\).
The solution set is the set of all real numbers, which can be written in interval notation as \((-\infty,\infty)\).

Answer:

\((-\infty,\infty)\)