Question

Factor out the greatest common factor from the following polynomial.4x^7 - 20x^6 + 8x^5

Answer 1

The given polynomial is:

$4x^7-20x^6+8x^5$

Notice that the greatest common factor of the numbers 4, 20, and 8 is 4.

Also, notice that the greatest common factor of the variables is x⁵.

Hence, the greatest common factor of the polynomial is 4x⁵.

Therefore factor out 4x⁵ from the polynomial to get:

$\begin{gathered} 4x^7-20x^6+8x^5=4x^5(\frac{4x^7}{4x^5}-\frac{20x^6}{4x^5}+\frac{8x^5}{4x^5}) \\ =4x^5(x^2-5x+8) \end{gathered}$