anonymous
  • anonymous
Just wanted to check my answers if they are right. (See below)
Mathematics
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anonymous
  • anonymous
Just wanted to check my answers if they are right. (See below)
Mathematics
jamiebookeater
  • jamiebookeater
See more answers at brainly.com
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anonymous
  • anonymous
1.)\[\frac{ x-4 }{ x^2-3x-4 }\]
anonymous
  • anonymous
My answer: \[\frac{ 1 }{ (x+1) }\]
anonymous
  • anonymous
1 is correct

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anonymous
  • anonymous
Thanks! 2.) \[\frac{ x^3-8 }{ x-2 }\]
anonymous
  • anonymous
My answer:\[(x+2)^2\]
anonymous
  • anonymous
I think u can simplify more than that
anonymous
  • anonymous
How would I simplify that?
anonymous
  • anonymous
hold on
anonymous
  • anonymous
something is wrong
anonymous
  • anonymous
I don't think I factored the numerator right.
anonymous
  • anonymous
start by putting the 8 into 2^3
anonymous
  • anonymous
Okay. Then what?
anonymous
  • anonymous
and use the difference of cubes which is \[a^3−b^3=(a−b)(a^2+ab+b^2)\]
anonymous
  • anonymous
it will get you \[(x−2)(x^2+(x)(2)+2^2)\]
anonymous
  • anonymous
Simplify 2^2 to 4 and regroup terms
anonymous
  • anonymous
\[\frac{ (x−2)(x^2+2x+4) }{ x-2 }\]
anonymous
  • anonymous
now just cancel the x-2
anonymous
  • anonymous
did you get it?
anonymous
  • anonymous
Ya I got it. Wasn't that the same answer I got?
anonymous
  • anonymous
\[(x+2)^2\]
anonymous
  • anonymous
It's different
anonymous
  • anonymous
I wrote the same answer.
anonymous
  • anonymous
\[x^2+2x +4 \neq (x+2)^2\]
anonymous
  • anonymous
Ya sorry about that. Just noticed.
anonymous
  • anonymous
I would have to use the quadratic formula for this right?
Zale101
  • Zale101
\(a^3-b^3=(x-a)(a^2+ab+b^2)\) \(x^3-2^3=(x-2)(x^2+2x+2^2)=x^2+2x+4\) \(\Large\frac{x^3-8}{x-2}=\frac{x^2-2^3}{x-2}=\frac{(x-2)(x^2+2x+4)}{x-2}\)
Zale101
  • Zale101
\(\Large =x^2+2x+4\)
anonymous
  • anonymous
Ya I got that so far. Thanks!
anonymous
  • anonymous
\[\frac{ -2\pm \sqrt{2^2-4(1)(4)} }{ 2(1) }\]\[\frac{ -2\pm \sqrt{4-16} }{ 2 }\]\[\frac{ -2\pm \sqrt{-12} }{ 2 }\]
anonymous
  • anonymous
The answer is going to have an i?
Zale101
  • Zale101
Yes. That's why it cant be factored. If you get complex numbers when factoring, then the polynomial is irreducible. x^2+2x+4 is a prime polynomial.
anonymous
  • anonymous
So I don't have to simplify that then? Do I just put x^2+2x+4?
Zale101
  • Zale101
Yes :)
anonymous
  • anonymous
Alright thanks! 3.)\[\frac{ 5-x }{ x^2-25 }\]
anonymous
  • anonymous
My answer:\[\frac{ -1 }{ x+5 }\]
anonymous
  • anonymous
4.) \[\frac{ x^2-4x-32 }{ x^2-16 }\]
alekos
  • alekos
3 is correct
anonymous
  • anonymous
My answer:\[\frac{ x-8 }{ x-4 }\]
anonymous
  • anonymous
Thanks! What about #4?
alekos
  • alekos
yes. well done
anonymous
  • anonymous
Thanks you guys!

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