Factor the following expression completely. y^13+y Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. y^13+y=square B. The polynomial is prime.

To factor the expression \( y^{13} + y \) completely, we can start by factoring out the greatest common factor (GCF). <br /><br />The GCF of \( y^{13} \) and \( y \) is \( y \).<br /><br />So, we factor out \( y \):<br /><br />\[<br />y^{13} + y = y(y^{12} + 1)<br />\]<br /><br />Next, we need to check if \( y^{12} + 1 \) can be factored further. Notice that \( y^{12} + 1 \) is a sum of two terms, but it does not fit any standard factoring formulas like the difference of squares or sum/difference of cubes.<br /><br />Therefore, the complete factorization of the given polynomial is:<br /><br />\[<br />y^{13} + y = y(y^{12} + 1)<br />\]<br /><br />So, the correct choice is:<br />A. \( y^{13} + y = y(y^{12} + 1) \)