Part A:

Question

How can the following equation be re-written if you factor out the Greatest Common Factor?

3x2−15x=0
3
𝑥
2
−
15
𝑥
=
0


(1 point)
Responses

3x(x+5)=0
3
𝑥
(
𝑥
+
5
)
=
0
3 x open paren x plus 5 close paren is equal to 0

3x(x−5)=0
3
𝑥
(
𝑥
−
5
)
=
0
3 x open paren x minus 5 close paren is equal to 0

3x(x−15)=0
3
𝑥
(
𝑥
−
15
)
=
0
3 x open paren x minus 15 close paren is equal to 0

5x(x−5)=0
5
𝑥
(
𝑥
−
5
)
=
0
5 x open paren x minus 5 close paren is equal to 0
Question 2
Part B:

What would the two solutions be?

(1 point)
Responses

x=0 and x=5
𝑥
=
0


𝑎
𝑛
𝑑

𝑥
=
5
x=0 and x=5
𝑥
=
0


𝑎
𝑛
𝑑

𝑥
=
5

x=0
𝑥
=
0

x=0
𝑥
=
0


x=5
𝑥
=
5
x is equal to 5

x=0 and x=−5

Answer 1

Part A:

To factor out the Greatest Common Factor (GCF) from the equation \(3x^2 - 15x = 0\):

1. Identify the GCF of the terms \(3x^2\) and \(15x\). The GCF is \(3x\).

2. Factor out \(3x\):

   \[ 3x(x - 5) = 0 \]

So, the correct response is: 3x(x−5)=0.

---

Part B:

To find the solutions of the equation \(3x(x - 5) = 0\), we set each factor equal to zero:

1. \(3x = 0\) gives \(x = 0\).
2. \(x - 5 = 0\) gives \(x = 5\).

Thus, the two solutions are:

x=0 and x=5.