Which of the following is an x-intercept of the function, \( f(x)=x^{3}+3 x^{2}-10 x-24 \) ? A. 4 B. 2 c. -4 D. -3

To find the x-intercept of the function \( f(x)=x^{3}+3 x^{2}-10 x-24 \), we need to determine where \( f(x) = 0 \). By substituting the given options into the equation: - For \( x = 4 \): \( f(4) = 4^3 + 3(4^2) - 10(4) - 24 = 64 + 48 - 40 - 24 = 48 \) (not an x-intercept) - For \( x = 2 \): \( f(2) = 2^3 + 3(2^2) - 10(2) - 24 = 8 + 12 - 20 - 24 = -24 \) (not an x-intercept) - For \( x = -4 \): \( f(-4) = (-4)^3 + 3(-4)^2 - 10(-4) - 24 = -64 + 48 + 40 - 24 = 0 \) (this is an x-intercept!) - For \( x = -3 \): \( f(-3) = (-3)^3 + 3(-3)^2 - 10(-3) - 24 = -27 + 27 + 30 - 24 = 6 \) (not an x-intercept) Thus, the x-intercept of the function is \( -4 \), corresponding to option c.