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)