Question

1. factor $-8b - 4$.

a. $-4(2b + 1)$
b. $-2(4b + 2)$
c. $-4b - 4$
d. $-8(b + 0.5)$

Explanation:

Step1: Identify greatest common factor

The terms are $-8b$ and $-4$. The greatest common factor (GCF) of $8$ and $4$ is $4$, and since both terms are negative, we factor out $-4$.

Step2: Divide each term by the GCF

For $-8b$: $\frac{-8b}{-4} = 2b$
For $-4$: $\frac{-4}{-4} = 1$

Step3: Write factored form

Combine the GCF and the results: $-4(2b + 1)$

Step4: Verify other options

Option b: $-2(4b+2)$ can be factored further (GCF of 2 remains inside), so it is not fully factored.
Option c: $-4b-4$ is the original expression rearranged, not factored.
Option d: $-8(b+0.5)$ uses a decimal, which is not the standard integer-based factoring for this problem.

Answer:

a. $-4(2b + 1)$