xpand the expression to a polynomial in standard form: \[ (4 x-5)\left(x^{2}+4 x+1\right) \]

To expand the expression \((4x - 5)(x^2 + 4x + 1)\), let's distribute each term in the first binomial to every term in the second trinomial. First, we'll distribute \(4x\): \[ 4x \cdot x^2 = 4x^3 \\ 4x \cdot 4x = 16x^2 \\ 4x \cdot 1 = 4x \] Now, we'll distribute \(-5\): \[ -5 \cdot x^2 = -5x^2 \\ -5 \cdot 4x = -20x \\ -5 \cdot 1 = -5 \] Now, combine all these results together: \[ 4x^3 + 16x^2 + 4x - 5x^2 - 20x - 5 \] Next, we combine like terms: \[ 4x^3 + (16x^2 - 5x^2) + (4x - 20x) - 5 \] \[ = 4x^3 + 11x^2 - 16x - 5 \] Thus, the polynomial in standard form is: \[ \boxed{4x^3 + 11x^2 - 16x - 5} \]