For the polynomial below, 1 is a zero. \[ h(x)=x^{3}-3 x^{2}-2 x+4 \] Express \( h(x) \) as a product of linear factors. \( h(x)=\square \)

To express \( h(x) = x^{3} - 3x^{2} - 2x + 4 \) as a product of linear factors, we can first use synthetic division to divide the polynomial by \( (x - 1) \), since 1 is a zero: \[ \begin{array}{r|rrr} 1 & 1 & -3 & -2 & 4 \\ & & 1 & -2 & -4 \\ \hline & 1 & -2 & -4 & 0 \\ \end{array} \] This gives us the quotient: \[ h(x) = (x - 1)(x^{2} - 2x - 4) \] Next, we can factor \( x^{2} - 2x - 4 \) using the quadratic formula: \[ x = \frac{-(-2) \pm \sqrt{(-2)^{2} - 4(1)(-4)}}{2(1)} = \frac{2 \pm \sqrt{4 + 16}}{2} = \frac{2 \pm \sqrt{20}}{2} = 1 \pm \sqrt{5} \] Thus, the factors of the polynomial can be expressed as: \[ h(x) = (x - 1)(x - (1 + \sqrt{5}))(x - (1 - \sqrt{5})) \] Therefore, \( h(x) \) can be written as: \[ h(x) = (x - 1)(x - (1 + \sqrt{5}))(x - (1 - \sqrt{5})) \]