Question

Factor it completely
13x^11-117x^3

Answer 1

To factor the expression \( 13x^{11} - 117x^3 \) completely, we can follow these steps:

1. **Factor out the greatest common factor (GCF):**
In this expression, both terms share a common factor of \( 13x^3 \).

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

2. **Factor the difference of squares:**
The expression \( x^8 - 9 \) can be factored further, as it is a difference of squares:

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

3. **Combine the factors:**
Substituting back, we have:

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

Since \( x^4 - 3 \) and \( x^4 + 3 \) do not factor further using real coefficients, we conclude our factorization here.

Thus, the completely factored form of the expression is:

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