Question

Factor the polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be​ factored, so state.
12x + 16
Select the correct choice below and fill in any answer boxes within your choice.
12x + 16 = blank
The polynomial is prime.

Answer 1

To factor the polynomial \(12x + 16\) using the greatest common factor (GCF), we first find the GCF of the coefficients 12 and 16.

The factors of 12 are: \(1, 2, 3, 4, 6, 12\)
The factors of 16 are: \(1, 2, 4, 8, 16\)
The greatest common factor of 12 and 16 is \(4\).

Now we can factor out the GCF:

\[
12x + 16 = 4(3x + 4)
\]

Thus, the factored form is:

\[
12x + 16 = 4(3x + 4)
\]

So, the complete answer is:

\[
12x + 16 = 4(3x + 4)
\]