Use the method of long division and synthetic division and synthetic division to factorize.
\[
\begin{array}{l}
x^{3}-3 x^{2}-4 x+12 \\
8 x^{4}-64 x=0
\end{array}
\]
Answer
\(\boxed{8 x^{4}-64 x = 8x(x - 2)(x^{2} + 2x + 4)}\)
Step 1 ：We are given two polynomials: \(x^{3}-3 x^{2}-4 x+12\) and \(8 x^{4}-64 x=0\).
Step 2 ：We need to factorize these polynomials.
Step 3 ：For the first polynomial, we can use the method of synthetic division to find its factors.
Step 4 ：The factors of the first polynomial are \((x - 3)(x - 2)(x + 2)\).
Step 5 ：For the second polynomial, we can factorize it by taking out the common factor.
Step 6 ：The factors of the second polynomial are \(8x(x - 2)(x^{2} + 2x + 4)\).
Step 7 ：\(\boxed{x^{3}-3 x^{2}-4 x+12 = (x - 3)(x - 2)(x + 2)}\)
Step 8 ：\(\boxed{8 x^{4}-64 x = 8x(x - 2)(x^{2} + 2x + 4)}\)
