Question

factor out the coefficient of the variable term.

1. $6n - 24$
2. $\frac{1}{2}q + \frac{5}{2}$
3. $-4x + 36$

Explanation:

Step1: Analyze the expression \(6n - 24\)

Find the greatest common factor (GCF) of \(6n\) and \(24\). The GCF of \(6\) and \(24\) is \(6\).

Step2: Factor out the GCF

Using the distributive property \(ab+ac = a(b + c)\), we factor out \(6\) from \(6n-24\):
\(6n-24=6(n - 4)\)

Step1: Analyze the expression \(\frac{1}{2}q+\frac{5}{2}\)

The coefficient of the variable term \(\frac{1}{2}q\) is \(\frac{1}{2}\). We factor out \(\frac{1}{2}\) from both terms.

Step2: Factor out the coefficient

\(\frac{1}{2}q+\frac{5}{2}=\frac{1}{2}(q + 5)\)

Step1: Analyze the expression \(- 4x+36\)

The GCF of \(-4x\) and \(36\) is \(- 4\) (we can also use \(4\), but factoring out \(-4\) keeps the coefficient of \(x\) positive inside the parentheses).

Step2: Factor out the GCF

\(-4x + 36=-4(x-9)\) (we can also write it as \(4(-x + 9)\), but factoring out \(-4\) is a common approach to make the coefficient of \(x\) positive inside the parentheses)

Answer:

1. \(6(n - 4)\)
2. \(\frac{1}{2}(q + 5)\)
3. \(-4(x - 9)\) (or \(4(-x + 9)\))