Answer:
Option A is correct
5 is a factor of [tex]5x^3-135[/tex]
Step-by-step explanation:
To factor the [tex]5x^3-135[/tex]
we can write 135 as:
[tex]135 =5 \cdot 3^3[/tex]
then;
[tex]5x^3-5 \cdot 3^3[/tex]
Take 5 common we have;
[tex]5(x^3-3^3)[/tex]
using identity rule:
[tex](x^3-a^3) = (x-a)(x^2+ax+a^2)[/tex]
\then;
[tex]5 \cdot (x-3) \cdot (x^2-3x+9)[/tex]
⇒the factor of [tex]5x^3-135[/tex] are: 5, x-3 and [tex]x^2-3x+9[/tex]
Therefore, from the given options the following factor of [tex]5x^3-135[/tex] is, only 5
