Question

1. $x^2 - 3x - x = 0$

Explanation:

Step1: Combine like terms

First, we combine the \( -3x \) and \( -x \) terms in the equation \( x^2 - 3x - x = 0 \). Combining these like terms gives us \( x^2 - 4x = 0 \).

Step2: Factor out the common factor

Next, we factor out the common factor \( x \) from the left - hand side of the equation \( x^2 - 4x = 0 \). Factoring out \( x \) gives us \( x(x - 4)=0 \).

Step3: Solve for x using the zero - product property

The zero - product property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \) (or both). So, for the equation \( x(x - 4)=0 \), we set each factor equal to zero:

• If \( x = 0 \), the equation is satisfied.
• If \( x - 4=0 \), then we solve for \( x \) by adding 4 to both sides of the equation, which gives us \( x = 4 \).

Answer:

The solutions are \( x = 0 \) and \( x = 4 \)