To find \((f \circ g)(x)\), we need to substitute \(g(x)\) into \(f(x)\).
Given:
- \(f(x) = 3x + 14\)
- \(g(x) = 2x^2 - 4x + 1\)
Now we will substitute \(g(x)\) into \(f(x)\):
\[ f(g(x)) = f(2x^2 - 4x + 1) \]
Now, replace \(x\) in \(f(x)\) with \(g(x)\):
\[ f(g(x)) = 3(2x^2 - 4x + 1) + 14 \]
Now, distribute \(3\):
\[ = 3 \cdot 2x^2 - 3 \cdot 4x + 3 \cdot 1 + 14 \] \[ = 6x^2 - 12x + 3 + 14 \]
Now combine like terms:
\[ = 6x^2 - 12x + 17 \]
Thus, the polynomial expression for \((f \circ g)(x)\) in standard form is:
\[ \boxed{6x^2 - 12x + 17} \]