Questions: Question Factor to find all (x)-intercepts of the function. [ f(x)=-9 x^4-3 x^3 ]

Factor the function \( f(x) = -9x^{4} - 3x^{3} \) to find all \( x \)-intercepts.

Factor out the greatest common factor (GCF).

The GCF of \( -9x^{4} \) and \( -3x^{3} \) is \( -3x^{3} \). Factoring out \( -3x^{3} \) gives: \[ f(x) = -3x^{3}(3x + 1) \]

Set the factored function equal to zero to find the \( x \)-intercepts.

Set \( f(x) = 0 \): \[ -3x^{3}(3x + 1) = 0 \] This equation is satisfied when either \( -3x^{3} = 0 \) or \( 3x + 1 = 0 \).

Solve \( -3x^{3} = 0 \).

Divide both sides by \( -3 \): \[ x^{3} = 0 \] Take the cube root of both sides: \[ x = 0 \]

Solve \( 3x + 1 = 0 \).

Subtract 1 from both sides: \[ 3x = -1 \] Divide both sides by 3: \[ x = -\frac{1}{3} \]

The \( x \)-intercepts are \( \boxed{x = 0} \) and \( \boxed{x = -\frac{1}{3}} \).

The \( x \)-intercepts of the function \( f(x) = -9x^{4} - 3x^{3} \) are: \[ \boxed{x = 0} \] \[ \boxed{x = -\frac{1}{3}} \]