Factor polynomials

[Desan65]

How do you factor 3x to the 4th power minus 27x to the second power?
My answer was 3x to the second power (x to the second power minus 9), but my teacher said that it was incorrect.

 

[mathwannabe]

First, lets rewrite the problem using the latex code.

\(\displaystyle 3x^4-27x^2=\) ................First, lets see if we can use the distributive law

\(\displaystyle =3x^2(x^2-9)\) ...............3x^2 is the common factor for both terms

\(\displaystyle =3x^2(x-3)(x+3)\) ......Here we use difference of squares to further factor the brackets


You see, your answer was correct, but it was incomplete. After you use difference of squares, you will have complete answer.

 

[mathwannabe]

Your teacher should have said that you were ok to that point, but that you could factor further...

I agree. Your answer was not wrong, it was just incomplete. Your math teacher should have told you that.