Question

solve for x:
x³ = 3x²
choose the best answer with all solutions
hint: set equation = 0 first then factor the gcf

○ x= 1/3, 0

○ x=0

○ x = 0, 3

○ x = -1, 1, 3, 0

Explanation:

Step1: Move all terms to one side

To solve the equation \(x^{3}=3x^{2}\), we first subtract \(3x^{2}\) from both sides to set the equation to zero. This gives us \(x^{3}-3x^{2}=0\).

Step2: Factor out the GCF

The greatest common factor (GCF) of \(x^{3}\) and \(3x^{2}\) is \(x^{2}\). Factoring out \(x^{2}\) from the left - hand side, we get \(x^{2}(x - 3)=0\).

Step3: Apply the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). So, for \(x^{2}(x - 3)=0\), we have two cases:

• Case 1: \(x^{2}=0\). Taking the square root of both sides, we find that \(x = 0\) (with multiplicity 2).
• Case 2: \(x-3=0\). Solving for \(x\), we add 3 to both sides and get \(x = 3\).

Answer:

\(x = 0,3\) (corresponding to the option "x = 0, 3")