Part A:

Question

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

3x2−15x=0

(1 point)
Responses

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

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

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

5x(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 and x=5

x=0
x=0

x=5
x is equal to 5

x=0 and x=−5

Answer 1

Part A:

To factor the equation \( 3x^2 - 15x = 0 \), first, we find the greatest common factor (GCF) of the coefficients 3 and -15, which is 3. We can also factor out \( x \) from the two terms.

Factoring, we have:

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

So, the correct response is:

3x(x - 5) = 0

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Part B:

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

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

Thus, the two solutions are:

x = 0 and x = 5