Factor -30f-60g+15 using the GCF.
A. 15(-2f-4g+1)
B. 6(-5f-10g+3)
C. 3(-10f-20g+5)
D. 5(-6-12g+3)
To factor the expression -30f - 60g + 15 using the Greatest Common Factor (GCF), we need to find the largest integer that can divide each of the coefficients without leaving a remainder.
The numbers we're looking at are -30, -60, and 15. The GCF of these numbers is 15 since 15 can be divided into each of them without leaving a remainder:
- 30 / 15 = -2
- 60 / 15 = -4
- 15 / 15 = 1
It also appears that the GCF should be negative because our leading term is negative (-30f), and we want to factor out a negative to keep the leading term positive in the factored form.
So let's factor out -15:
-15(2f) -15(4g) + -15(-1) = -15(2f + 4g - 1)
The negative signs in the factors are due to taking out a negative GCF; that ensures that when we redistribute, we get the original expression back:
-15 * 2f = -30f
-15 * 4g = -60g
-15 * (-1) = +15
The proper factored expression using the GCF would be:
-15(2f + 4g - 1)
This option is not explicitly listed in A, B, C, or D above. However, let's adjust the expression to match one of these options:
We can distribute the negative inside the parenthesis to get a visually equivalent expression:
-15(-2f - 4g + 1)
This matches option A:
A. 15(-2f - 4g + 1)
Hence, the factored expression of -30f - 60g + 15 using the GCF is option A.