If px = x^2 + 1 and qx = 5x + 1, which expression is equivalent to p * qx?

To find the expression equivalent to p * qx, we first need to substitute the given expressions for p and qx into the equation.

We’re given:

• px = x² + 1

So, when we multiply p by qx, we have:

p * qx = (x² + 1)(5x + 1)

Now we can expand this expression:

Using the distributive property (also known as the FOIL method for binomials), we multiply each term in the first expression by each term in the second:

• (x² * 5x) + (x² * 1) + (1 * 5x) + (1 * 1)

Calculating these gives us:

• 5x³ + x² + 5x + 1

Therefore, the expression equivalent to p * qx is:

5x³ + x² + 5x + 1