Kipress your answer as a polynomial in standard form. \[ \begin{array}{r}f(x)=x+5 \\ g(x)=x^{2}-4 x+8 \\ \text { Find: } g(f(x))\end{array} \]

To find \( g(f(x)) \), we need to substitute \( f(x) = x + 5 \) into \( g(x) \). First, recall the function \( g(x) \): \[ g(x) = x^2 - 4x + 8 \] Now, substitute \( f(x) \) into \( g(x) \): \[ g(f(x)) = g(x + 5) \] This means we replace every \( x \) in \( g(x) \) with \( x + 5 \): \[ g(x + 5) = (x + 5)^2 - 4(x + 5) + 8 \] Now let's compute each term: 1. Expand \( (x + 5)^2 \): \[ (x + 5)^2 = x^2 + 10x + 25 \] 2. Expand \( -4(x + 5) \): \[ -4(x + 5) = -4x - 20 \] Now we can put it all together: \[ g(x + 5) = (x^2 + 10x + 25) - (4x + 20) + 8 \] Combine like terms: \[ = x^2 + 10x + 25 - 4x - 20 + 8 \] \[ = x^2 + (10x - 4x) + (25 - 20 + 8) \] \[ = x^2 + 6x + 13 \] So, the polynomial \( g(f(x)) \) in standard form is: \[ \boxed{x^2 + 6x + 13} \]