Question

Solve the quadratic equation 46x2−138x=0 by factoring out the GCF.(1 point)
Responses

The solutions are x=−3 and x=46.
The solutions are x equals negative 3 and x equals 46 .

The solutions are x=−46 and x=3.
The solutions are x equals negative 46 and x equals 3 .

The solutions are x=0 and x=3.
The solutions are x equals 0 and x equals 3 .

The solutions are x=0 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.

1. The GCF of \(46x^2\) and \(-138x\) is \(46x\).
2. We can factor out \(46x\) from the equation:

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

3. Now we can set each factor equal to zero:

\[
46x = 0 \quad \text{or} \quad x - 3 = 0
\]

4. Solving these gives us:

- From \(46x = 0\):
\[
x = 0
\]

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

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

The correct response is:

The solutions are \(x = 0\) and \(x = 3\).