f(x) = x2 + 8x +15 8(x) = x+ 5 Fn ({ •g) (x) x + 68x2 + 75 x° + 13x2 + 55x + 75 x +23x2 +45x+ 75 x + 13x' + 55x + 20

It seems that your notation and expressions are a bit jumbled. I'll help you break them down step by step. First, let's clarify what you have: 1. **Function**: \( f(x) = x^2 + 8x + 15 \) 2. Another expression: \( 8(x) = x + 5 \) - this looks like it might be a function notation that isn’t standard. 3. You have expressions involving \( F \) and \( g \), but they need clarification. Let's start by analyzing \( f(x) \): ### Step 1: Factor \( f(x) \) We can factor \( f(x) \): \[ f(x) = x^2 + 8x + 15 = (x + 3)(x + 5) \] ### Step 2: The other function notation It’s unclear what you meant by \( 8(x) = x + 5 \). If you're referring to a function \( g(x) = x + 5 \), let's rewrite that. ### Step 3: Clarifying other functions You wrote a series of expressions involving \( Fn \), \( g \), and more polynomials. Here’s what I can suggest based on the context: 1. If you're trying to apply operations to \( f(x) \) or evaluate functions at certain values, please specify. 2. If you’re looking for a composite function, you might be asking for \( f(g(x)) \) or similar operations. ### If you need to combine functions: For example, if you want to compose \( f \) with \( g \): \[ g(x) = x + 5 \] Then \( f(g(x)) \) becomes: \[ f(g(x)) = f(x + 5) = (x + 5)^2 + 8(x + 5) + 15 \] Calculating this: \[ = (x^2 + 10x + 25) + (8x + 40) + 15 \] \[ = x^2 + 18x + 80 \] ### Step 4: Clarification on remaining expressions For the remaining expressions: - Please clarify if they are additional functions, computations you want to perform, or something else. Feel free to provide more details, and I can assist you further!