Explanation:
To find the GCF (greatest common factor) of the two terms, we need to factor them each into their prime factors and determine which factors they have in common. However, upon inspection, we can see that both terms have a common factor of 2, so we can factor that out:
2x^2 + 30x + 88 = 2(x^2 + 15x + 44)
2x^3 + 7x^2 - 4x = 2x(x^2 + 3.5x - 2)
Now we can simplify the fraction by dividing out the common factor of 2:
(2(x^2 + 15x + 44)) / (2x(x^2 + 3.5x - 2)) = (x^2 + 15x + 44) / (x(x^2 + 3.5x - 2))
To fit the given format, we can write:
(x^2 + 15x + 44) = (x + ___)(x + ___)
Using FOIL method, we can find the factors that give us x^2 + 15x + 44:
(x + 11)(x + 4)
Therefore, the new expression in the numerator once the GCF had been factored is:
(x + 11)(x + 4)