Answer:
[tex]3x^4 - 3x ^3 - 18x ^2=3x^2(x+2)(x-3).[/tex]
Step-by-step explanation:
The expression [tex]3x^4 - 3x ^3 - 18x ^2[/tex] consists of three terms:
- [tex]3x^4;[/tex]
- [tex]-3x^3;[/tex]
- [tex]-18x^2.[/tex]
These three terms have common factor [tex]3x^2.[/tex] Thus,
[tex]3x^4 - 3x ^3 - 18x ^2=3x^2(x^2-x-6).[/tex]
Consider the expression [tex]x^2-x-6.[/tex] You can rewrite it as
[tex]x^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)=(x+2)(x-3).[/tex]
The whole expression takes look
[tex]3x^4 - 3x ^3 - 18x ^2=3x^2(x+2)(x-3).[/tex]
