Factor the following high-degree polynomial completely.

Question

13x11−117x3


(1 point)
Responses

13x3(x4−3)(x4+3)
13 x cubedeft parenthesis x squared minus 8 right parenthesis left parenthesis x superscript 4 baseline plus 3 right parenthesis

13x3(x2−3)(x2+3)(x4+3)
13 x cubed left parenthesis x squared minus 3 right parenthesis left parenthesis x squared plus 3 right parenthesis left parenthesis x superscript 4 baseline plus 3 right parenthesis

13x3(x4−92)(x4+92)
13 x cubed left parenthesis x superscript 4 baseline minus Start Fraction 9 over 2 End Fraction right parenthesis left parenthesis x superscript 4 baseline plus Start Fraction 9 over 2 End Fraction right parenthesis

13x3(x8−9)

Answer 1

To factor the polynomial \(13x^{11} - 117x^3\) completely, we can first factor out the greatest common factor (GCF), which is \(13x^3\):

\[ 13x^{11} - 117x^3 = 13x^3(x^{8} - 9) \]

Next, we can observe that \(x^{8} - 9\) is a difference of squares. We can factor it as follows:

\[ x^{8} - 9 = (x^{4})^2 - 3^2 = (x^4 - 3)(x^4 + 3) \]

Putting this all together, we have:

\[ 13x^{11} - 117x^3 = 13x^3(x^{4} - 3)(x^{4} + 3) \]

Thus, the complete factorization of the given polynomial is:

\[ \boxed{13x^3(x^4 - 3)(x^4 + 3)} \]