anonymous
  • anonymous
How does: r^3+3r^2-4 = (r-1)(r^2+4r+4) ?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
multiply it out... r^3 + 4r^2 + 4r - r^2 - 4r - 4 = r^3 + 3r^2 - 4. Got it?
anonymous
  • anonymous
Yes, but given the polynomial r^3 + 3r^2 - 4, how do you factor it to become (r-1)(r^2+4r+4)?
anonymous
  • anonymous
use long division. (r^3+3r^2-4)/(r-1)

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anonymous
  • anonymous
Look for a root by trial and error. Possible roots are the factors of 4, which are 1, -1, 2, -2, and 4, -4. Always try first "1". Plug in 1 into r^3 + 3r^2 - 4 and you'll get 0. That means that "r - 1" is a factor. then divide r^3 + 3r^2 - 4 by "r - 1" and you'll get r^2+4r+4.
anonymous
  • anonymous
That makes sense, thank you!

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