The choices below are all factors. Choose the THREE factors from the choices below which can be multiplied together to yield the following expression: x^3+5x^2-4x-20 D (x+2) (x-20) (x^2+4) (x-5) (x-4) (x+4) (x^2+5) (x-2) (x+5)

To find the factors of the expression $x^{3}+5x^{2}-4x-20$, we can use polynomial long division or synthetic division to divide the expression by one of the factors and see if we get a quadratic expression. Let's try dividing by $(x-2)$:<br /><br />\[<br />\begin{array}{r|rrrr}<br />x-2 & x^3 & +5x^2 & -4x & -20 \\<br />\hline<br /> & x^2 & +7x & +10 \\<br />\end{array}<br />\]<br /><br />The quotient is $x^2 + 7x + 10$, which is a quadratic expression. Now, we can factor this quadratic expression:<br /><br />\[<br />x^2 + 7x + 10 = (x+2)(x+5)<br />\]<br /><br />So, the factors of the original expression $x^{3}+5x^{2}-4x-20$ are $(x-2)$, $(x+2)$, and $(x+5)$. Therefore, the correct choices are:<br /><br />D $(x+2)$<br />$(x-5)$<br />$(x-4)$