To understand how to work with polynomial functions using substitution, let’s break it down step by step.

First, you need to know what a polynomial function looks like. For example, let’s look at this one:

f(x) = 2x² + 3x - 5

When we say we are going to substitute, it means we will put a specific number in place of x.

Let’s go through the steps:

1. Pick a Number: Let’s say we want to find f(2). This means we will use 2 for x.

2. Substitute: Now, replace every x in the function with 2. This makes the equation look like this:

   f(2) = 2(2)² + 3(2) - 5

3. Do the Math: Now, we’ll calculate this step by step:

   • First, calculate 2(2)²:
     • 2² is 4, so 2 times 4 equals 8.
   • Next, calculate 3(2):
     • 3 times 2 equals 6.
   • Finally, we put it all together:
     • 8 (from the first part) + 6 (from the second part) - 5 equals 9.

So, f(2) equals 9!

See? It’s pretty easy once you understand the steps!