Which factorization is equivalent to this expression?

Question

−42k−54
(1 point)
Responses

−6(7k−9)
negative 6 times open paren 7 k minus 9 close paren

6(−7k+9)
6 times open paren negative 7 k plus 9 close paren

−6(7k+9)
negative 6 times open paren 7 k plus 9 close paren

6(7k+9)
6 times open paren 7 k plus 9 close paren

Answer 1

To factor the expression \(-42k - 54\), we can start by identifying the greatest common factor (GCF) of the coefficients \(-42\) and \(-54\).

1. The factors of \(-42\) are \(-2, -3, -6, -7, -14, -21\).
2. The factors of \(-54\) are \(-2, -3, -6, -9, -18, -27\).

The GCF of \(42\) and \(54\) is \(6\). Therefore, we can factor \(6\) out of the expression:

\[ -42k - 54 = -6(7k + 9) \]

Now, since we want to write it correctly, we notice that we factor out \(-6\):

So, \[ -42k - 54 = -6(7k + 9) \]

Thus, the factorization equivalent to the expression \(-42k - 54\) is:

\(-6(7k + 9)\)

The closest match to this choice is: \(\text{-6(7k+9)}\)

So the correct answer is: \(-6(7k + 9)\)