Factoring Questions - Confermation

[Math_Junkie]

Factor Fully:

1) x^12 - x^9
= x^3 (x^9 - x^6)

2) (x + 2)^2 - 49
= (x+2+7) (x+2-7)
= (x+9)(x-5)

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

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Just wondering if these solutions are correct?

 

[galactus]

2 and 3 look good. The first one needs a little tweaking yet.

\(\displaystyle \L\\x^{12}-x^{9}\)

Factor out x^9:

\(\displaystyle \L\\x^{9}(x^{3}-1)\)

Now, we have the difference of two cubes:

\(\displaystyle \L\\x^{3}-1=(x-1)(x^{2}+x+1)\)

\(\displaystyle \fbox{\H\\x^{9}(x-1)(x^{2}+x+1)}\)

See?.

 

[Math_Junkie]

I just knew there was a trick to that question.
It didn't seem to be factored fully haha!
Thank you very much!
Understood!