your results numerically. \[ \text { e. }(x+5)\left(x^{2}+5 x-3\right) \]

To solve for \( (x+5)(x^2 + 5x - 3) \) numerically, you can expand the expression using the distributive property (also known as the FOIL method for binomials). Start by multiplying \( x \) by each term in the second polynomial and then do the same for \( 5 \). 1. \( x \cdot (x^2 + 5x - 3) = x^3 + 5x^2 - 3x \) 2. \( 5 \cdot (x^2 + 5x - 3) = 5x^2 + 25x - 15 \) Now combine these results: \[ x^3 + 5x^2 - 3x + 5x^2 + 25x - 15 \] Combine like terms: \[ x^3 + 10x^2 + 22x - 15 \] So the final expanded form is: \[ x^3 + 10x^2 + 22x - 15 \] This expression can now be analyzed or evaluated for specific values of \( x \). For example, plugging in \( x = 1 \): \[ 1^3 + 10(1^2) + 22(1) - 15 = 1 + 10 + 22 - 15 = 18 \] You can easily plug in other values for \( x \) and see how this cubic polynomial behaves!