Solving Quadratic Equations Using Common Factors Quick Check

Question

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Question
Solve the quadratic equation 5x2+75x=0 by factoring out the GCF.(1 point)
Responses

The solutions are x=−15 and x=−5.
The solutions are x equals negative 15 and x equals negative 5 .

The solutions are x=−15 and x=0.
The solutions are x equals negative 15 and x equals 0 .

The solutions are x=0 and x=15.
The solutions are x equals 0 and x equals 15 .

The solutions are x=0 and x=5.

Answer 1

To solve the quadratic equation \( 5x^2 + 75x = 0 \) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms.

The GCF of \( 5x^2 \) and \( 75x \) is \( 5x \).

Now, we factor out \( 5x \) from the equation:

\[ 5x(x + 15) = 0 \]

Next, we set each factor equal to zero:

1. \( 5x = 0 \)
2. \( x + 15 = 0 \)

For the first equation:

\[ 5x = 0 \implies x = 0 \]

For the second equation:

\[ x + 15 = 0 \implies x = -15 \]

Therefore, the solutions to the equation are:

\[ x = 0 \quad \text{and} \quad x = -15 \]

The correct answer is:

The solutions are \( x = -15 \) and \( x = 0 \).