Question

factor each expression using the greatest common factor.
8x - 28 = \boxed{\quad}(\boxed{\quad} - \boxed{\quad})
12x + 15 = \boxed{\quad}(\boxed{\quad} + \boxed{\quad})

Explanation:

For \(8x - 28\):

Step1: Find GCF of 8 and 28

Factors of 8: \(1, 2, 4, 8\)
Factors of 28: \(1, 2, 4, 7, 14, 28\)
GCF is \(4\).

Step2: Divide each term by GCF

\(\frac{8x}{4} = 2x\), \(\frac{28}{4} = 7\)
So, \(8x - 28 = 4(2x - 7)\)

For \(12x + 15\):

Step1: Find GCF of 12 and 15

Factors of 12: \(1, 2, 3, 4, 6, 12\)
Factors of 15: \(1, 3, 5, 15\)
GCF is \(3\).

Step2: Divide each term by GCF

\(\frac{12x}{3} = 4x\), \(\frac{15}{3} = 5\)
So, \(12x + 15 = 3(4x + 5)\)

Answer:

For \(8x - 28\): \(4\), \(2x\), \(7\)
For \(12x + 15\): \(3\), \(4x\), \(5\)

(In boxed form as per each blank:
\(8x - 28 = \boxed{4}(\boxed{2x} - \boxed{7})\)
\(12x + 15 = \boxed{3}(\boxed{4x} + \boxed{5})\))