What is the equivalent expression for the product of p and qx if p is defined as px = x^2 + 1 and qx as qx = 5x + 1?

To find the expression equivalent to pq(x), we first need to interpret the given definitions of p and q.

We have:

• p: px = x^2 + 1
• q: qx = 5x + 1

Now, let’s compute the product pq(x):

Substituting the expressions for p and q into the product gives:

pq(x) = (x^2 + 1)(5x + 1)

Next, we will expand this expression using the distributive property:

pq(x) = (x^2 + 1)(5x + 1) 
= x^2 * 5x + x^2 * 1 + 1 * 5x + 1 * 1
= 5x^3 + x^2 + 5x + 1

Thus, we simplify this to reach the final answer:

The equivalent expression for pq(x) is:

5x^3 + x^2 + 5x + 1