How do you factor 3x^4-3? Can you please help me? I need to answer this. Thankyou.

Question

hartnn · Answer

can you first factor out 3 from 
3x^4-3 
?

mathstudent55 · Answer

First always look  for a common factor.
Then look at number of terms:
If 2 terms, try difference of squares or sum or difference of cubes.

anonymous · Answer

hartnn, thankyou! I'll try that!

hartnn · Answer

good! 
if you get stuck, we'll be here to help :)

anonymous · Answer

Thankyou!!
I always need help with my Math homework XD I'm not that good but I am willing to learn.

hartnn · Answer

oh, and bdw,
$\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} $

anonymous · Answer

Thankyou! That's very nice of you :">

anonymous · Answer

Is the answer 3(x^2+1)(x^2-1) ?

hartnn · Answer

you are on right path!
but notice that you can further factor x^2-1 :)

mathstudent55 · Answer

So far, so good, but after you factor, you need to check each factor to see if you can factor some more.

anonymous · Answer

So I have to factor it again? I'm kinda stuck XDD

hartnn · Answer

same thing what you have done, 
$a^2-b^2= (a+b)(a-b) \ (x^2-1^2) =... ?$

mathstudent55 · Answer

Look at each factor, and try this again:
If 2 terms, try difference of squares or sum or difference of cubes.

anonymous · Answer

Thankyou both! :)) I'll try that right now! Thanks. You're both great help!

anonymous · Answer

For x^2-1 is it (x+1)(x-1) ?

hartnn · Answer

correct :)

anonymous · Answer

Thankyou.
I still have to figure out x^2 + 1. I'm stuck again XDD. haha.

hartnn · Answer

now are you aware of imaginary numbers ? [if not, keep x^2+1 as it is]
or does this belong to imaginary/complex numbers ?

anonymous · Answer

I'm not really aware of it... Sorry

hartnn · Answer

x^2+1 does not have real factors, here, lets assume real factorization
so, your final answer will be 
$\large 3 (x+1)(x-1)(x^2+1)$
thats it!

anonymous · Answer

Thankyou so much

hartnn · Answer

you are most welcome ^_^

mathstudent55 · Answer

$$3x^4 - 3$$
$$=3(x^4 - 1)$$
$$=3(x^2 + 1)(x^2 -1)$$
$$=3(x^2 + 1)(x + 1)(x - 1)$$

hartnn · Answer

if and when you learn imaginary numbers, x^2+1 will be factorized as $(x+i)(x-i)$
till then , you can ignore this :)

anonymous · Answer

Thankyou both! I'm moving on to the next problem. Thankyousomuch for helping me with this. :))

mathstudent55 · Answer

wlcm

anonymous · Answer

x^6 + 26x^3 - 27 is it equal to : (x^3 + 27)(x^3 - 1) ?

mathstudent55 · Answer

Yes, but you're not done with factoring. Look at both binomials.

mathstudent55 · Answer

If 2 terms, try difference of squares or sum or difference of cubes.

mathstudent55 · Answer

@MoeshaKiel 
Did you finish this problem?

anonymous · Answer

Yes. I did. Thanks to the both of you :)) you were awesome help!

mathstudent55 · Answer

ok, wlcm