Question

Solve 5x2−40x=0
5
𝑥
2
−
40
𝑥
=
0
by factoring out the greatest common factor. Enter your solutions as an integer.(2 points)
x =
𝑥

=


x=
𝑥
=

Answer 1

To solve the equation \( 5x^2 - 40x = 0 \) by factoring out the greatest common factor, we first identify the GCF of the two terms.

The terms are \( 5x^2 \) and \( -40x \).
The GCF is \( 5x \).

We can factor out \( 5x \) from the equation:

\[
5x(x - 8) = 0
\]

Now, using the zero product property, we can set each factor equal to zero:

1. \( 5x = 0 \)
2. \( x - 8 = 0 \)

Solving these equations gives:

1. \( x = 0 \)
2. \( x = 8 \)

Thus, the solutions are:

\[
x = 0 \quad \text{and} \quad x = 8
\]

So the final answer is:
- \( x = 0 \)
- \( x = 8 \)