Answer:
Option D, -(x + 8)(x + 6) or,
-1(x + 8)(x + 6)
Step-by-step explanation:
The first step in the factorization of this polynomial is to factor our the negative from each term by dividing them by -1. This will make it easier for the next step:
-x² - 14x - 48 = -(x² + 14x + 48) or -1(x² + 14x + 48)
This negative will follow the factorization process to the answer, so any options without a negative in it can be discarded. This includes option C.
Now, we focus on the polynomial within the parentheses. To start factoring polynomials in the form quadratic expression form ax² + bx + c, we must find the factors from the product of coefficient a and constant c whose sum is equal to coefficient b. I promise it sounds more complicated than it is.
Coefficient a = 1
Coefficient b = 14
Constant c = 48
a(b) = 1(48) = 48
Now, we list factors of 48 to find which pair has a sum of 14:
1, 48; 2, 24; 3, 16; 4, 12; 6, 8
The last pair in 6 and 8 satisfy the parameters of being factors of 48 with a sum of 14. Therefore, we will substitute these values as coefficients for b, separate the terms into binomials, and factor out their greatest common factor (GCF):
-(x² + 6x + 8x + 48)
-[(x² + 6x) + (8x + 48)]
The GCF of x² and 6x is x. The GCF of 8x and 48 is 8.
-[x(x + 6) + 8(x + 6)]
If the binomial within the parentheses match each other, you have successfully found the factors. They are the binomial in the parentheses and the GCFs that were factored out:
-(x + 6)(x + 8) or -1(x + 6)(x + 8), option D.