Question

factor: $-8 + 24n$
a. $8(-4 + 12n)$
b. $-8(1 - 3n)$
c. $-8n(1 - 3n)$
d. $-8(1 + 3n)$
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Explanation:

Step1: Find the GCF of -8 and 24n

The greatest common factor (GCF) of -8 and 24n is -8.

Step2: Factor out -8 from the expression

We factor out -8 from \(-8 + 24n\). When we factor out -8 from -8, we get 1 (because \(\frac{-8}{-8}=1\)). When we factor out -8 from 24n, we get -3n (because \(\frac{24n}{-8}=-3n\))? Wait, no, wait. Wait, actually, let's do it correctly. The original expression is \(-8 + 24n\). Let's factor out -8. So, \(-8\times1 + (-8)\times(-3n)\). Because \(-8\times1=-8\) and \(-8\times(-3n)=24n\). So, factoring out -8, we get \(-8(1 - 3n)\). Let's check the options. Option B is \(-8(1 - 3n)\). Let's verify by expanding option B: \(-8\times1 + (-8)\times(-3n)=-8 + 24n\), which matches the original expression. Let's check other options: Option A: \(8(-4 + 12n)=-32 + 96n\), not matching. Option C: \(-8n(1 - 3n)=-8n + 24n^2\), not matching. Option D: \(-8(1 + 3n)=-8 - 24n\), not matching. So the correct answer is B.

Answer:

B. \(-8(1 - 3n)\)