Which factorization is equivalent to this expression?: -42k-54 A. -6 (7k - 9) B. 6 (-7k + 9) C. -6 (7k + 9) D. 6 (7k + 9)
The factorization that is equivalent to the expression -42k-54 is C. -6 (7k + 9).
To factorize the expression -42k - 54, we need to find the greatest common factor (GCF) of the terms -42k and -54.
Step 1: Start by finding the GCF of the coefficients. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The GCF of 42 and 54 is 6.
Step 2: Divide each term by the GCF. Dividing -42k by 6 gives -7k, and dividing -54 by 6 gives -9.
Therefore, we can factorize the expression -42k - 54 as -6(7k + 9).
So, the correct answer is C. -6 (7k + 9).
To determine which factorization is equivalent to the expression -42k - 54, we can start by factoring out the greatest common factor (GCF) of the terms, if any. In this case, both -42k and -54 are divisible by -6.
Step 1: Factor out the GCF (-6):
-42k - 54 = -6(7k + 9)
So, the factorization equivalent to the expression -42k - 54 is -6(7k + 9).
Therefore, the correct answer is A. -6 (7k + 9).