Factor the following high-degree polynomial completely.

Question

13x11−117x3


(1 point)
Responses

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

13x3(x8−9)
13 x cubed left parenthesis x superscript 8 baseline minus 9 right parenthesis

13x3(x4−92)(x4+92)

Answer 1

To factor the polynomial \(13x^{11} - 117x^3\) completely, we can start by factoring out the greatest common factor (GCF).

1. First, we can factor out \(13x^3\): \[ 13x^{11} - 117x^3 = 13x^3(x^{8} - 9) \]

2. Now, we will focus on factoring \(x^{8} - 9\). This expression is a difference of squares: \[ x^{8} - 9 = (x^{4})^2 - 3^2 = (x^{4} - 3)(x^{4} + 3) \]

3. Putting it all together, we have: \[ 13x^{11} - 117x^3 = 13x^3(x^{4} - 3)(x^{4} + 3) \]

Thus, the complete factorization of the polynomial is: \[ \boxed{13x^3(x^{4} - 3)(x^{4} + 3)} \]