When a student was directed to factor x^4 - 81 completely, his teacher did not give him full credit when he answered (x^2 + 9 )(x^2 - 9 . The student argued that because his answer does indeed give x^4 - 81 when multiplied out, he should be given full credit. Was the teacher justified in her grading of this problem? Why or why not? (HELP!) :X

Question

When a student was directed to factor x^4 - 81 completely, his teacher did not give him full credit when he answered (x^2 + 9 )(x^2 - 9 . The student argued that because his answer does indeed give x^4 - 81 when multiplied out, he should be given full credit.  Was the teacher justified in her grading of this problem? Why or why not? (HELP!) :X

skullpatrol · Answer

It is NOT factored COMPLETELY.

anonymous · Answer

I figured that but I did the problem.. and I can't really see what's wrong with it.. Either I'm missing something that's really simple there or I'm just getting confused by myself.. lol.

skullpatrol · Answer

You are missing the difference of two squares.

anonymous · Answer

Can you be more.. i mean more specific as to what the problem is missing.. I'm currently finishing a whole math packet and I got a headache.. ._.

skullpatrol · Answer

$$x^2 - 9$$$$=x^2-3^2$$$$=(x+3)(x-3)$$

anonymous · Answer

so when x^4 - 81 is partially right, it needed to be simplified further?

anonymous · Answer

was that all?

skullpatrol · Answer

Yep

anonymous · Answer

ahh wow, well, thanks for the help. ><

skullpatrol · Answer

np :)