Mathematics
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OpenStudy (anonymous):
factor step by step factor 32x^6 – 162.
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OpenStudy (anonymous):
yay!
OpenStudy (anonymous):
\[32x^6-162\]
factor out gcf
\[2(16x^6-81)\]
OpenStudy (anonymous):
ok
OpenStudy (anonymous):
ONE SEC
OpenStudy (anonymous):
is that a perfect square?
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OpenStudy (anonymous):
its a difference of squares
OpenStudy (anonymous):
o ok
OpenStudy (anonymous):
so it is \[2(4x^3+9)(4x^3-9)\]
OpenStudy (anonymous):
but notice we are not done
OpenStudy (anonymous):
why not
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OpenStudy (anonymous):
well \[ 4x^2+9\] won't factor but the other will. Do you see it?
OpenStudy (anonymous):
because its negitive
OpenStudy (anonymous):
yes
OpenStudy (anonymous):
ok so then what
OpenStudy (anonymous):
it is another difference of squares try and factor it
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OpenStudy (anonymous):
2x+3)(2x-3
OpenStudy (anonymous):
yep so all together it would be?
OpenStudy (anonymous):
no idea
OpenStudy (anonymous):
wait wait wait
OpenStudy (anonymous):
you said 4x^2+9 instead of 4x^3 +9
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OpenStudy (anonymous):
crap
OpenStudy (anonymous):
i blame the small writing
OpenStudy (anonymous):
so what do i do after i get 4x^3-9
OpenStudy (anonymous):
Over the rationals the answer is
\[
2 \left(4 x^3-9\right) \left(4
x^3+9\right)
\]
OpenStudy (anonymous):
what are the factors
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OpenStudy (anonymous):
i wrote that
OpenStudy (anonymous):
If you allow irrationals, we can factor further.
OpenStudy (anonymous):
i just miss read myself later
OpenStudy (anonymous):
true that
OpenStudy (anonymous):
what are the factors
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OpenStudy (anonymous):
exactly what he wrote above
OpenStudy (anonymous):
The factors are
\[
2\\ (-9 + 4 x^3) \\(9 + 4 x^3)
\]
OpenStudy (anonymous):
3 factors?
OpenStudy (anonymous):
yes
OpenStudy (anonymous):
thats just the factored form?
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OpenStudy (anonymous):
yes
OpenStudy (anonymous):
could you help me with another problom
OpenStudy (anonymous):
close this problem and ask a new one.
OpenStudy (anonymous):
eliassaab wants more medals
OpenStudy (anonymous):
jkjk
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OpenStudy (anonymous):
opend a new one