A) Solve the quadratic equation 46x

Question

2 − 138x = 0 by factoring out the GCF. (1 point)
The solutions are x = 0 and x = 46.
The solutions are x = − 46 and x = 3.
The solutions are x = 0 and x = 3.
The solutions are x = − 3 and x = 46

Answer 1

To solve the quadratic equation \(46x^2 - 138x = 0\) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms in the equation.

The GCF of \(46x^2\) and \(-138x\) is \(46x\).

We can factor out \(46x\) from the equation:

\[ 46x(x - 3) = 0 \]

Now, we set each factor equal to zero:

1. \(46x = 0\)
   This gives us \(x = 0\).

2. \(x - 3 = 0\)
   This gives us \(x = 3\).

Thus, the solutions to the equation are \(x = 0\) and \(x = 3\).

The correct answer is: The solutions are x = 0 and x = 3.