Question

Find the x-intercepts of the polynomial function. f(x)=x^6-63x^3-64

Answer 1

To find your x-intercepts, set f(x)=0, so 0=x^6-63x^3-64. You can do this by factoring x^6-63x^3-64 into $(x^3-64)(x^3+1)$, giving you $(x^3-64)(x^3+1)=0$. Next, solve each factor for x if f(x)=0, so $(x^3-64)=0$ and $(x^3+1)=0$. Solving for x gives you $x= \sqrt[3]{64} =4$ and $x= \sqrt[3]{-1}=-1$, meaning your x-intercepts are (4,0) and (-1,0)