Question

(a) The solutions of the equation $x^2\left(x-4\right)=0$are ___ .

(b)To solve the equation$x^3-4x^2=0$, we ___ the left-hand side.

Short answer

(a) The solutions of the equation $x^2\left(x-4\right)=0$ are 0, 0, 4

(b) To solve the equation $x^3-4x^2=0$, we factorize the left-hand side.

Step-by-step solution

Part a. Step 1. Apply the concept of factoring.

Factoring means finding expressions that can be multiplied together to give the expression on one side of the equation. If a quadratic equation can be factored, it is written as a product of linear terms.

Part a. Step 2. Analyze the given expression.

Given

$x^2\left(x-4\right)=0$

This is an equation of degree 3.

Part a. Step 3. Solve.

Solve the equation:

$\begin{array}{l}{x}^2\left(x-4\right)=0\\ \Rightarrow x^2=0\text{or}x-4=0\\ \Rightarrow x=0,x=0\text{or}x=4\end{array}$

Part b. Step 1. Apply the concept of factoring.

Factoring means finding expressions that can be multiplied together to give the expression on one side of the equation. If a quadratic equation can be factored, it is written as a product of linear terms.

Part b. Step 2. Analyze the given expression.

Given

$x^3-4x^2=0$

This is an equation of degree 3.

Part b. Step 3. Solve.

To solve the equation, we will first factorize the Left Hand Side and then solve as in part (a)