Question

Solve the quadratic equation 3x2−12x=0 by factoring for GCF(1 point) Responses The solutions are x=3 and x=4 The solutions are x is equal to 3 and x is equal to 4 The solutions are x=0 and x=4 The solutions are x is equal to 0 and x is equal to 4 The solutions are x=−4 and x=0 The solutions are x is equal to negative 4 and x is equal to 0 The solutions are x=−4 and x=3

Answer 1

To solve the quadratic equation \( 3x^2 - 12x = 0 \) by factoring for the greatest common factor (GCF), we first recognize that both terms on the left can be divided by 3 and \( x \).

1. Factor out the GCF: \[ 3x(x - 4) = 0 \]

2. Set each factor equal to zero: \[ 3x = 0 \quad \text{or} \quad x - 4 = 0 \]

3. Solve each equation:

   • From \( 3x = 0 \): \[ x = 0 \]
   • From \( x - 4 = 0 \): \[ x = 4 \]

Thus, the solutions are \( x = 0 \) and \( x = 4 \).

The correct response is: The solutions are x is equal to 0 and x is equal to 4.