Question
Factor this expression completely.
-42k - 54
-42k - 54
Answers
GPT-4o mini
To factor the expression \(-42k - 54\) completely, we can start by finding the greatest common factor (GCF) of the two terms.
First, let's find the GCF of the coefficients \(-42\) and \(-54\):
- The prime factorization of \(-42\) is \( -1 \times 2 \times 3 \times 7\).
- The prime factorization of \(-54\) is \( -1 \times 2 \times 3^3\).
The GCF is the product of the lowest powers of all prime factors:
- The GCF of the numbers is \( -1 \times 2 \times 3 = -6\).
Next, we can factor out \(-6\) from both terms in the expression:
\[
-42k - 54 = -6(7k + 9)
\]
Thus, the completely factored form of the expression \(-42k - 54\) is:
\[
-6(7k + 9)
\]
First, let's find the GCF of the coefficients \(-42\) and \(-54\):
- The prime factorization of \(-42\) is \( -1 \times 2 \times 3 \times 7\).
- The prime factorization of \(-54\) is \( -1 \times 2 \times 3^3\).
The GCF is the product of the lowest powers of all prime factors:
- The GCF of the numbers is \( -1 \times 2 \times 3 = -6\).
Next, we can factor out \(-6\) from both terms in the expression:
\[
-42k - 54 = -6(7k + 9)
\]
Thus, the completely factored form of the expression \(-42k - 54\) is:
\[
-6(7k + 9)
\]