Part A:

Question

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

12x2−18x=0
12
𝑥
2
−
18
𝑥
=
0

(1 point)
Responses

6x(2x+3)=0
6
𝑥
(
2
𝑥
+
3
)
=
0
6 x open paren 2 x plus 3 close paren is equal to 0

x(12x−18)=0
𝑥
(
12
𝑥
−
18
)
=
0
x times open paren 12 x minus 18 close paren is equal to 0

6x(12x−3)=0
6
𝑥
(
12
𝑥
−
3
)
=
0
6 x open paren 12 x minus 3 close paren is equal to 0

6x(2x−3)=0
6
𝑥
(
2
𝑥
−
3
)
=
0
6 x open paren 2 x minus 3 close paren is equal to 0
Question 2
Part B:

What would the two solutions be?

(1 point)
Responses

x=0 and x=23
𝑥
=
0

𝑎
𝑛
𝑑


𝑥
=
2
3
x=0 and x=23
𝑥
=
0

𝑎
𝑛
𝑑


𝑥
=
2
3

x=0 and x=32
𝑥
=
0

𝑎
𝑛
𝑑


𝑥
=
3
2
x=0 and x=32
𝑥
=
0

𝑎
𝑛
𝑑


𝑥
=
3
2

x=32
𝑥
=
3
2
x is equal to 3 halves

x=0 and x=−32
𝑥
=
0

𝑎
𝑛
𝑑


𝑥
=
−
3
2
x=0 and x=−32

Answer 1

To solve the problem, let's go through the steps for both Part A and Part B.

Part A

We start with the equation: \[ 12x^2 - 18x = 0 \]

To factor out the Greatest Common Factor (GCF), we first identify the GCF of the coefficients 12 and 18, which is 6.

Now we can factor out \(6x\): \[ 6x(2x - 3) = 0 \]

So the correct response for Part A is: 6x(2x−3)=0

---

Part B

Now, we need to find the solutions by setting the factored expression equal to zero: \[ 6x(2x - 3) = 0 \]

This gives us two factors:

1. \( 6x = 0 \)
2. \( 2x - 3 = 0 \)

Solving these:

1. From \( 6x = 0 \): \[ x = 0 \]

2. From \( 2x - 3 = 0 \): \[ 2x = 3 \] \[ x = \frac{3}{2} \]

Thus, the two solutions are: \[ x = 0 \quad \text{and} \quad x = \frac{3}{2} \]

So the correct response for Part B is: x=0 and x=32 (where \(32\) represents \( \frac{3}{2} \)).

Therefore, the two parts are correctly answered as:

• Part A: \(6x(2x−3)=0\)
• Part B: \(x=0 \text{ and } x=\frac{3}{2}\) (interpreted as \(x=32\)).