To factor out the greatest common factor (GCF) from the polynomial [tex]\( 47j^2 + 6 \)[/tex], we need to follow these steps:
1. Identify the coefficients: The coefficients in the polynomial [tex]\( 47j^2 + 6 \)[/tex] are 47 and 6.
2. Find the GCF of the coefficients:
- The prime factorization of 47 is [tex]\( 47 \)[/tex] (since 47 is a prime number).
- The prime factorization of 6 is [tex]\( 2 \times 3 \)[/tex].
Since the greatest common divisor (GCD) of 47 and 6 is 1, the GCF is 1.
3. Factor the polynomial:
- When the GCF of the coefficients is 1, the polynomial cannot be factored further by common factors.
- Therefore, the polynomial remains as it is.
So the factored form of the polynomial [tex]\( 47j^2 + 6 \)[/tex] is simply:
[tex]\[ 47j^2 + 6 \][/tex]
This indicates that there are no common factors to factor out other than 1, and thus the polynomial is already in its simplest form.
