Question

factor completely 4x^5 - 20x^4 - 36x^3.
4(x^5 - 5x^4 - 9x^3)
x^3(4x^2 - 20x - 36)
x^2 - 5x - 9
4x^3(x^2 - 5x - 9)

Explanation:

Step1: Find the GCF of coefficients

The coefficients are 4, -20, -36. The GCF of 4, 20, 36 is 4.

Step2: Find the GCF of variable - terms

The variable - terms are \(x^{5}\), \(x^{4}\), \(x^{3}\). The GCF of \(x^{5}\), \(x^{4}\), \(x^{3}\) is \(x^{3}\).

Step3: Factor out the GCF

Factor out \(4x^{3}\) from \(4x^{5}-20x^{4}-36x^{3}\):
\[

$$\begin{align*} 4x^{5}-20x^{4}-36x^{3}&=4x^{3}\times x^{2}-4x^{3}\times5x - 4x^{3}\times9\\ &=4x^{3}(x^{2}-5x - 9) \end{align*}$$

\]

Answer:

D. \(4x^{3}(x^{2}-5x - 9)\)