Part A:

Question

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

12x2−18x=0

(1 point)
Responses

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

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

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

6x(2x−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 and x=23

x=0 and x=32
x=0 and x=32

x=32
x is equal to 3 halves

x=0 and x=−32

Answer 1

Part A:

To factor the equation \(12x^2 - 18x = 0\), we first find the Greatest Common Factor (GCF) of the two terms. The GCF of \(12x^2\) and \(-18x\) is \(6x\).

Now, we can factor this out:

\[ 12x^2 - 18x = 6x(2x - 3) = 0 \]

So the correct option is:

6x(2x - 3) = 0

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Part B:

To find the solutions, we set each factor equal to zero:

1. \(6x = 0\) implies \(x = 0\).
2. \(2x - 3 = 0\) implies \(2x = 3\) or \(x = \frac{3}{2}\).

Thus, the two solutions are:

x = 0 and x = \frac{3}{2}

So the corresponding response is:

x = 0 and x = \frac{3}{2}.