Question

factor to find all x-intercepts of the function.
$f(x) = x^3 - 5x$
answer attempt 1 out of 2
additional solution no solution
$x = $
submit answer

Explanation:

Step1: Factor out the common term

We can factor out an \(x\) from the function \(f(x)=x^{3}-5x\). So we get \(f(x)=x(x^{2} - 5)\).

Step2: Set each factor equal to zero

To find the \(x\)-intercepts, we set \(f(x) = 0\). This gives us two equations:

1. \(x=0\)
2. \(x^{2}-5 = 0\)

For the second equation \(x^{2}-5=0\), we can solve for \(x\) by adding 5 to both sides and then taking the square root. So \(x^{2}=5\), which gives \(x=\pm\sqrt{5}\)

Answer:

\(x = 0\), \(x=\sqrt{5}\), \(x = -\sqrt{5}\)