If \( f(x)=x^{2}+8 x+3 \), what is \( f(x+3) \) ? (Simplify your answer complete.............................................................................. \( f(x+3)=\square \) TUTORIAL

1. The function is given by \[ f(x) = x^2 + 8x + 3. \] 2. To find \( f(x+3) \), substitute \( x+3 \) for \( x \) in the function: \[ f(x+3) = (x+3)^2 + 8(x+3) + 3. \] 3. Expand \((x+3)^2\): \[ (x+3)^2 = x^2 + 6x + 9. \] 4. Expand the term \(8(x+3)\): \[ 8(x+3) = 8x + 24. \] 5. Substitute the expanded terms back into the expression: \[ f(x+3) = x^2 + 6x + 9 + 8x + 24 + 3. \] 6. Combine like terms: \[ f(x+3) = x^2 + (6x + 8x) + (9 + 24 + 3). \] 7. Simplify: \[ f(x+3) = x^2 + 14x + 36. \] Thus, the simplified expression for \( f(x+3) \) is \[ \boxed{x^2 + 14x + 36}. \]