anonymous
  • anonymous
how do you factor a^2^n +6a^n+8
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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abb0t
  • abb0t
Just to be clear, is it really a\(\sf\color{red}{^{2n}}\)+a\(\sf\color{red}{^{n}}\)+8?
anonymous
  • anonymous
yes
anonymous
  • anonymous
6a^n sorry

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abb0t
  • abb0t
Rewrite it using LaTex (the equation editor) on the bottom of this little box.
anonymous
  • anonymous
\[a ^{2n}+6a ^{n}+8\]
abb0t
  • abb0t
Well, are you solving for \(a\) or for \(n\)?
anonymous
  • anonymous
It says to factor completely or indicate if prime
abb0t
  • abb0t
Well, eitheway, what two numbers when multiplied give you 8, but when added equal 6?
abb0t
  • abb0t
I am going to assume that n = some number (for simplicity, i will assume n = 1)
anonymous
  • anonymous
ok
abb0t
  • abb0t
Are you with me so far? B/c 6 or 8 is nOT the answer.
anonymous
  • anonymous
yes
abb0t
  • abb0t
Well, what are those two numbers @red32968 ___ \(\times\) ___ = 8 ___ + ___ = 6
anonymous
  • anonymous
4*2 4+2
abb0t
  • abb0t
Yes, Correct! So you have: a\(^{2n}\)+4a\(^n\)+2a\(^n\)+8, next you will group them (a\(^{2n}\)+4a\(^n\))+(2a\(^n\)+8). Notice you can factor out a few terms for them. Correct? Factor those terms out for me.
abb0t
  • abb0t
HINT: x\(^{2b}\)+x\(^b\) = x\(^b\)(x\(^b\)+1)....it's good to remember your exponent rules here.
abb0t
  • abb0t
NOTE: x\(^b\)(x\(^b\))= x\(^{b+b}\)= x\(^{2b}\)
anonymous
  • anonymous
\[a ^{2n}(6^{an}+8)\]a ^{2n+n}
abb0t
  • abb0t
No, not quite.
anonymous
  • anonymous
where did I make the mistake
anonymous
  • anonymous
\[6a ^{n}\]
abb0t
  • abb0t
Here's another HINT: a\(^n\)(a\(^n\)+4) that is ONE of them.
anonymous
  • anonymous
the second should be \[a ^{n}(a ^{n}+8)\]
abb0t
  • abb0t
No! You can ONLY factor out a 2 from the second one!
anonymous
  • anonymous
2\[2(a ^{n}+8)\]
anonymous
  • anonymous
actually IT SHOULD BE +4
abb0t
  • abb0t
YES! Correct!
abb0t
  • abb0t
So, now that you have everything factored, what is your final answer? I can compare it.
abb0t
  • abb0t
(__ + __)(__ +__) what are the __ ?
anonymous
  • anonymous
\[A ^{N}(A ^{n}+4) 2 ( a^{n}+4)\]
abb0t
  • abb0t
Not quite, you forgot the +2, but the final answer is: \(\sf\color{red}{(a^n+2)(a^n+4)}\)
anonymous
  • anonymous
thank you for your patience and help

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