Question

How do you factor the expression -30n^2 + 288n - 384 using the Greatest Common Factor (GCF)?

a) -6n(n - 8)
b) 6n(n - 8)
c) -6(n - 8)(n + 8)
d) 6(n - 8)(n + 8)

Answer 1

The expression -30n^2 + 288n - 384 factors to -6(5n^2 - 48n + 64) after factoring out the greatest common factor of -6. The quadratic inside the parenthesis does not further factor over the integers.

Step-by-step explanation:

To factor the expression -30n^2 + 288n - 384 using the Greatest Common Factor (GCF), first identify the GCF of the coefficients. In this case, the GCF for 30, 288, and 384 is 6. Since the expression is negative, we factor out -6 to get:

-6(5n^2 - 48n + 64)

Now, let's try to factor the quadratic inside the parenthesis. However, notice that there is no pair of factors of 5*64 that sums up to -48, meaning that the quadratic does not factor nicely. Therefore, the original expression does not factor over the integers beyond pulling out the GCF of -6, and none of the options (a, b, c, d) provided are correct.

The GCF method that we used here is often more than 100 words and involves factoring out the largest common factor in each term of the polynomial. In summary, our expression factors to:

-6(5n^2 - 48n + 64)