Question

question 39 of 42
what is the greatest common factor (gcf) of the numerator and denominator in the rational expression below?
\\(\frac{7x + 14}{2x^2 + x - 6}\\)
\\(\bigcirc\\) a. \\(-6\\)
\\(\bigcirc\\) b. \\(2x - 3\\)
\\(\bigcirc\\) c. \\(x + 2\\)
\\(\bigcirc\\) d. \\(7\\)

Explanation:

Step1: Factor Numerator

Factor \(7x + 14\): \(7x + 14 = 7(x + 2)\)

Step2: Factor Denominator

Factor \(2x^2 + x - 6\). Using factoring: \(2x^2 + x - 6 = (2x - 3)(x + 2)\)

Step3: Identify GCF

The numerator is \(7(x + 2)\) and the denominator is \((2x - 3)(x + 2)\). The common factor is \(x + 2\).

Answer:

C. \(x + 2\)